According to the conjecture based on some known facts of integrable models, a new （2＋1）-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known （2＋1）-d...According to the conjecture based on some known facts of integrable models, a new （2＋1）-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known （2＋1）-dimensional negative Kadomtsev-Petviashvili equation but also the extension of the known （1＋1）-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac-Moody-Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.展开更多
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for...The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.展开更多
By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of ...By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.展开更多
Based on the bosonization approach, the supersymmetric Burgers(SB) system is transformed to a coupled bosonic system. By solving the bosonized SB(BSB) equation, the difficulties caused by the anticommutative fermionic...Based on the bosonization approach, the supersymmetric Burgers(SB) system is transformed to a coupled bosonic system. By solving the bosonized SB(BSB) equation, the difficulties caused by the anticommutative fermionic field of the SB equation can be avoided. The nonlocal symmetry for the BSB equation is obtained by the truncated Painlev′e method. By introducing multiple new fields, the finite symmetry transformation for the BSB equation is derived by solving the first Lie's principle of the prolonged systems. Some group invariant solutions are obtained with the similarity reductions related by the nonlocal symmetry.展开更多
Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symm...Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.展开更多
In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact sol...In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.展开更多
We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we c...We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we carry out a cluster mean-field analysis.Analytical results show that the densities of the two upstream segments of the intersection site are always equal,which indicates that the system is not in asymmetric phases.It demonstrates that the spontaneous symmetry breaking does not exist in the system.The density profiles and the boundaries of the symmetric phases are also investigated.We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.展开更多
An improved method is proposed for the extraction of the symmetry energy coefficient relative to the temperature,a_(sym)/T,in the heavy-ion reactions near the Fermi energy region,based on the modified Fisher Model.Thi...An improved method is proposed for the extraction of the symmetry energy coefficient relative to the temperature,a_(sym)/T,in the heavy-ion reactions near the Fermi energy region,based on the modified Fisher Model.This method is applied to the primary fragments of antisymmetrized molecular dynamics(AMD)simulations for ^(46)Fe+^(46)Fe,^(40)Ca+^(40)Ca and ^(48)Ca+^(48)Ca at 35 MeV/nucleon,in order to make direct comparison to the results from the K(N,Z)method of Ono et al.In our improved method,the extracted values of a_(sym)/T increase as the size of isotopes increases whereas,in the K(N,Z)method,the results show rather constant behavior.This increase in our result is attributed to the surface contribution of the symmetry energy in finite nuclei.In order to evaluate the surface contribution,the relation a_(sym)/T=[a_(sym)^((V))(1-k_(S/V) A^(-1/3))]/T is applied and k_(S/V)=1.20~1.25 was extracted.This value is smaller than those extracted from the mass table,reflecting the weakened surface contribution at higher temperature regime.Δμ/T,the difference of the neutron-proton chemical potentials relative to the temperature,is also extracted in this method at the same time.The average values of the extractedΔμ/T,Δμ/T show a linear dependence on the proton-neutron a_(sym)metry parameter of the system,δ_(sys),andΔμ/T=(15.1±0.2)δ_(sys)-(0.5±0.1)is obtained.展开更多
The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time dela...The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.展开更多
The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural...The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.展开更多
The purpose of this paper is threefold. One is to revisit the Hermitian form model (HFM) with Hermitian symmetry proposed by Chino and Shiraiwa (1993), which uncovers the latent Hilbert space structure or the indefini...The purpose of this paper is threefold. One is to revisit the Hermitian form model (HFM) with Hermitian symmetry proposed by Chino and Shiraiwa (1993), which uncovers the latent Hilbert space structure or the indefinite metric space structure, given the asymmetric similarity matrix (ASM) among objects, and another is to explain how to interpret the configuration of objects embedded in these spaces. The final goal of this paper is to show what kinds of information are obtained by applying HFM to empirical and hypothetical ASMs. Results of applications of HFM to two empirical ASMs suggest that some possible asymmetric structures among objects exist, which might not have been found empirically. The result of application of the HFM to a hypothetical ASM uncovers interesting latent space structures among objects.展开更多
Echinoderm radial symmetry has first appeared in the ambulacral system, when the ambulacral channel assumed the shape of a closed ring or a horseshoe with approximated ends, and then spread onto other organ systems. I...Echinoderm radial symmetry has first appeared in the ambulacral system, when the ambulacral channel assumed the shape of a closed ring or a horseshoe with approximated ends, and then spread onto other organ systems. Its origin was a natural consequence of a steady increase of the original asymmetry of bilaterally-asymmetric three-segmented ancestors of echinoderms, culminated by closing of the ancestral linear metamerism into radiality. The evolutionary transformation from a simple pouchlike hydrocoel with one side channel to an elongated hydrocoel (located under the oesophagus) with two side channels, and finally to a nearly closed horseshoeshaped hydrocoel with three radial channels can be reconstructed based on the theca structure and the number of ambulacra in the row SolutaCincta-Helicoplacoidea. After the hydrocoel with three outbound ambulacral channels circled around the oesophagus as a horseshoe, it either closed into a ring, or its ends became closely approximated. This has determined the primary triradiate symmetry, which quickly transformed into pentaradial symmetry of the 2-1-2 type as a result of branching of two of the three primary radial channels. This occurred no earlier than the Late Vendian, when the first bilaterians appeared to have begun to acquire body appendages, and no later than the Early Cambrian, when the first skeletal remains of echinoderms entered the fossil record (in the Atdabanian). The 2-1-2 pentaradial symmetry evolved into the true pentaradiality as a result of shifting the timing of tentacle branching to earlier stages of ontogenesis and even spreading of the five tentacle primordia over the ambulacral ring. This occurred during the Ordovician.展开更多
It is shown that the local counterterms which simultaneously restore local Lorentz and gauge invariance of the σ-model do not satisfy the criteria of(2,0)supersymmetry.But local counterterms and the non-local part of...It is shown that the local counterterms which simultaneously restore local Lorentz and gauge invariance of the σ-model do not satisfy the criteria of(2,0)supersymmetry.But local counterterms and the non-local part of one-loop effective action together are invariant under the(2,0)supersymmetry transformation.展开更多
It was recently noted that in certain nonmagnetic centrosymmetric compounds,spin–orbit interactions couple each local sector that lacks inversion symmetry,leading to visible spin polarization effects in the real spac...It was recently noted that in certain nonmagnetic centrosymmetric compounds,spin–orbit interactions couple each local sector that lacks inversion symmetry,leading to visible spin polarization effects in the real space,dubbed“hidden spin polarization(HSP)”.However,observable spin polarization of a given local sector suffers interference from its inversion partner,impeding material realization and potential applications of HSP.Starting from a single-orbital tight-binding model,we propose a nontrivial way to obtain strong sector-projected spin texture through the vanishing hybridization between inversion partners protected by nonsymmorphic symmetry.The HSP effect is generally compensated by inversion partners near the Г point but immune from the hopping effect around the boundary of the Brillouin zone.We further summarize 17 layer groups that support such symmetry-assisted HSP and identify hundreds of quasi-2D materials from the existing databases by first-principle calculations,among which a group of rare-earth compounds LnIO(Ln=Pr,Nd,Ho,Tm,and Lu)serves as great candidates showing strong Rashba-and Dresselhaus-type HSP.Our findings expand the material pool for potential spintronic applications and shed light on controlling HSP properties for emergent quantum phenomena.展开更多
We present a way to calculate the Witten indexΔfor a class of l+l dimensional supersymmetric(SUSY)models with O(N)symmetry.SinceΔis invariant under an adiabatic change of parameters,an O(N)non-invariant but SUSY ter...We present a way to calculate the Witten indexΔfor a class of l+l dimensional supersymmetric(SUSY)models with O(N)symmetry.SinceΔis invariant under an adiabatic change of parameters,an O(N)non-invariant but SUSY term 2hФN is added to the Lagrangian,therefore the degeneracy of zero-energy states due to O(N)symmetry is removed.It is shown that SUSY breaking can occur for the SUSY O(N)Wess-Zumino model.展开更多
The(400)stretching overtone band of AsH3 has been observed near 8029.0 cm^(-1) and analyzed in both symmetric and asymmetric top models.The results indicate that the dynamical symmetry of the(400)local mode state has ...The(400)stretching overtone band of AsH3 has been observed near 8029.0 cm^(-1) and analyzed in both symmetric and asymmetric top models.The results indicate that the dynamical symmetry of the(400)local mode state has reduced to that of an asymmetric top and the rotational energy levels can be assigned by a set of quantum numbers J,K_(a),and K_(c).展开更多
To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34)equation is found b...To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34)equation is found by means of a direct method.The related point symmetries can be obtained simply by taking the infinitesimal form of the finite point symmetry group.The point symmetries of the CKP34 equation constitute an infinite dimensional KacMoody-Virasoro algebra.The point symmetry invariant solutions of the CKP34 equation are obtained via the standard classical Lie point symmetry method.展开更多
The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé...The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.展开更多
The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the gener...The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the general form of the symmetry operators for AQRM-related models.Applying this ansatz we obtain the symmetry operator for three models:the anisotropic AQRM,the asymmetric Rabi–Stark model(ARSM),and the anisotropic ARSM.展开更多
In this work,the gyrokinetic eigenvalue code LIGKA,the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigen...In this work,the gyrokinetic eigenvalue code LIGKA,the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes(RSAEs).Using the parameters from an ASDEXUpgrade plasma,a benchmark with the three different physical models for RSAE without and with energetic particles(EPs)is carried out.Reasonable agreement has been found for the mode frequency and the growth rate.Mode structure symmetry breaking(MSSB)is observed when EPs are included,due to the EPs’non-perturbative effects.It is found that the MSSB properties are featured by a finite radial wave phase velocity,and the linear mode structure can be well described by an analytical complex Gaussian expressionФ(s)=e^(-σ(s-s_(0))^(2))with complex parametersσand s_(0),where s is the normalized radial coordinate.The mode structure is distorted in opposite manners when the EP drive shifted from one side of qminto the other side,and specifically,a non-zero average radial wave number with opposite signs is generated.The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport.The parallel velocity of EPs is generated in opposite directions,due to different values of the average radial wave number,corresponding to different initial EP density profiles with EP drive shifted away from the qmin.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10735030)the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. 20040969)+1 种基金the National Basic Research Programs of China (Grant Nos. 2007CB814800 and 2005CB422301)the PCSIRT (IRT0734)
文摘According to the conjecture based on some known facts of integrable models, a new （2＋1）-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known （2＋1）-dimensional negative Kadomtsev-Petviashvili equation but also the extension of the known （1＋1）-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac-Moody-Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.
基金Supported by the Global Change Research Program China under Grant No.2015CB953904the National Natural Science Foundations of China under Grant Nos.11435005,11175092,and 11205092+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213K.C.Wong Magna Fund in Ningbo University
文摘The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.
基金The Project supported by the Natural Science Foundation of Shandong Province of China under Grant No.Q2005A01
文摘By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675146,11305106,11472177,11275129the Natural Science Foundation of Zhejiang Province of China under Grant No.LZ15A050001
文摘Based on the bosonization approach, the supersymmetric Burgers(SB) system is transformed to a coupled bosonic system. By solving the bosonized SB(BSB) equation, the difficulties caused by the anticommutative fermionic field of the SB equation can be avoided. The nonlocal symmetry for the BSB equation is obtained by the truncated Painlev′e method. By introducing multiple new fields, the finite symmetry transformation for the BSB equation is derived by solving the first Lie's principle of the prolonged systems. Some group invariant solutions are obtained with the similarity reductions related by the nonlocal symmetry.
基金The project supported by National Natural Science Foundations of China under Grant Nos. 10735030, 10475055, and 90503006； the Natural Science Research Plan in Shaanxi Province under Grant No. SJ08A09； the Research Fund of Postdoctoral of China under Grant No. 20070410727；the Research Found of Shaanxi Normal University
文摘Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090the Natural Science Foundation of Shandong Province under Grant No.ZR2015AL008the High-Level Personnel Foundation of Liaocheng University under Grant No.31805
文摘In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.
基金Project supported by the National Natural Science Foundation of China(Grant No.11802003).
文摘We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we carry out a cluster mean-field analysis.Analytical results show that the densities of the two upstream segments of the intersection site are always equal,which indicates that the system is not in asymmetric phases.It demonstrates that the spontaneous symmetry breaking does not exist in the system.The density profiles and the boundaries of the symmetric phases are also investigated.We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.
文摘An improved method is proposed for the extraction of the symmetry energy coefficient relative to the temperature,a_(sym)/T,in the heavy-ion reactions near the Fermi energy region,based on the modified Fisher Model.This method is applied to the primary fragments of antisymmetrized molecular dynamics(AMD)simulations for ^(46)Fe+^(46)Fe,^(40)Ca+^(40)Ca and ^(48)Ca+^(48)Ca at 35 MeV/nucleon,in order to make direct comparison to the results from the K(N,Z)method of Ono et al.In our improved method,the extracted values of a_(sym)/T increase as the size of isotopes increases whereas,in the K(N,Z)method,the results show rather constant behavior.This increase in our result is attributed to the surface contribution of the symmetry energy in finite nuclei.In order to evaluate the surface contribution,the relation a_(sym)/T=[a_(sym)^((V))(1-k_(S/V) A^(-1/3))]/T is applied and k_(S/V)=1.20~1.25 was extracted.This value is smaller than those extracted from the mass table,reflecting the weakened surface contribution at higher temperature regime.Δμ/T,the difference of the neutron-proton chemical potentials relative to the temperature,is also extracted in this method at the same time.The average values of the extractedΔμ/T,Δμ/T show a linear dependence on the proton-neutron a_(sym)metry parameter of the system,δ_(sys),andΔμ/T=(15.1±0.2)δ_(sys)-(0.5±0.1)is obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No 10865006)
文摘The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.
基金Project supported by the Science Foundation from Education Department of Liaoning Province, China （Grant No 202142036） and the National Natural Science Foundation of China （Grant No 10475036）.
文摘The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
文摘The purpose of this paper is threefold. One is to revisit the Hermitian form model (HFM) with Hermitian symmetry proposed by Chino and Shiraiwa (1993), which uncovers the latent Hilbert space structure or the indefinite metric space structure, given the asymmetric similarity matrix (ASM) among objects, and another is to explain how to interpret the configuration of objects embedded in these spaces. The final goal of this paper is to show what kinds of information are obtained by applying HFM to empirical and hypothetical ASMs. Results of applications of HFM to two empirical ASMs suggest that some possible asymmetric structures among objects exist, which might not have been found empirically. The result of application of the HFM to a hypothetical ASM uncovers interesting latent space structures among objects.
文摘Echinoderm radial symmetry has first appeared in the ambulacral system, when the ambulacral channel assumed the shape of a closed ring or a horseshoe with approximated ends, and then spread onto other organ systems. Its origin was a natural consequence of a steady increase of the original asymmetry of bilaterally-asymmetric three-segmented ancestors of echinoderms, culminated by closing of the ancestral linear metamerism into radiality. The evolutionary transformation from a simple pouchlike hydrocoel with one side channel to an elongated hydrocoel (located under the oesophagus) with two side channels, and finally to a nearly closed horseshoeshaped hydrocoel with three radial channels can be reconstructed based on the theca structure and the number of ambulacra in the row SolutaCincta-Helicoplacoidea. After the hydrocoel with three outbound ambulacral channels circled around the oesophagus as a horseshoe, it either closed into a ring, or its ends became closely approximated. This has determined the primary triradiate symmetry, which quickly transformed into pentaradial symmetry of the 2-1-2 type as a result of branching of two of the three primary radial channels. This occurred no earlier than the Late Vendian, when the first bilaterians appeared to have begun to acquire body appendages, and no later than the Early Cambrian, when the first skeletal remains of echinoderms entered the fossil record (in the Atdabanian). The 2-1-2 pentaradial symmetry evolved into the true pentaradiality as a result of shifting the timing of tentacle branching to earlier stages of ontogenesis and even spreading of the five tentacle primordia over the ambulacral ring. This occurred during the Ordovician.
文摘It is shown that the local counterterms which simultaneously restore local Lorentz and gauge invariance of the σ-model do not satisfy the criteria of(2,0)supersymmetry.But local counterterms and the non-local part of one-loop effective action together are invariant under the(2,0)supersymmetry transformation.
基金National Natural Science Foundation of China(Grant No.11874195)the Guangdong Provincial Key Laboratory of Computational Science and Material Design(Grant No.2019B030301001)the Center for Computational Science and Engineering of SUSTech.
文摘It was recently noted that in certain nonmagnetic centrosymmetric compounds,spin–orbit interactions couple each local sector that lacks inversion symmetry,leading to visible spin polarization effects in the real space,dubbed“hidden spin polarization(HSP)”.However,observable spin polarization of a given local sector suffers interference from its inversion partner,impeding material realization and potential applications of HSP.Starting from a single-orbital tight-binding model,we propose a nontrivial way to obtain strong sector-projected spin texture through the vanishing hybridization between inversion partners protected by nonsymmorphic symmetry.The HSP effect is generally compensated by inversion partners near the Г point but immune from the hopping effect around the boundary of the Brillouin zone.We further summarize 17 layer groups that support such symmetry-assisted HSP and identify hundreds of quasi-2D materials from the existing databases by first-principle calculations,among which a group of rare-earth compounds LnIO(Ln=Pr,Nd,Ho,Tm,and Lu)serves as great candidates showing strong Rashba-and Dresselhaus-type HSP.Our findings expand the material pool for potential spintronic applications and shed light on controlling HSP properties for emergent quantum phenomena.
基金Supported by National Natural Science Foundation of Chinaby Fujian Nature Science Founda tion.
文摘We present a way to calculate the Witten indexΔfor a class of l+l dimensional supersymmetric(SUSY)models with O(N)symmetry.SinceΔis invariant under an adiabatic change of parameters,an O(N)non-invariant but SUSY term 2hФN is added to the Lagrangian,therefore the degeneracy of zero-energy states due to O(N)symmetry is removed.It is shown that SUSY breaking can occur for the SUSY O(N)Wess-Zumino model.
基金Supported by the National Natural Science Foundation of China under Grant No.29290304Chinese Academy of Sciences under Grant No.KMX85-17.
文摘The(400)stretching overtone band of AsH3 has been observed near 8029.0 cm^(-1) and analyzed in both symmetric and asymmetric top models.The results indicate that the dynamical symmetry of the(400)local mode state has reduced to that of an asymmetric top and the rotational energy levels can be assigned by a set of quantum numbers J,K_(a),and K_(c).
基金sponsored by the National Natural Science Foundations of China(Nos.11975131,11435005)
文摘To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34)equation is found by means of a direct method.The related point symmetries can be obtained simply by taking the infinitesimal form of the finite point symmetry group.The point symmetries of the CKP34 equation constitute an infinite dimensional KacMoody-Virasoro algebra.The point symmetry invariant solutions of the CKP34 equation are obtained via the standard classical Lie point symmetry method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11975131 and 11435005)the K C Wong Magna Fund in Ningbo University。
文摘The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.
基金the Australian Research Council(Grant Nos.DP170104934 and DP1801010)。
文摘The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the general form of the symmetry operators for AQRM-related models.Applying this ansatz we obtain the symmetry operator for three models:the anisotropic AQRM,the asymmetric Rabi–Stark model(ARSM),and the anisotropic ARSM.
基金partially within the EUROFUSION Enabling Research Projects Projects‘NLED’(ER15-ENEA-03)‘NAT’(Cf P-AWP17-ENRMPG-01)+2 种基金‘MET’(ENR-MFE19-ENEA-05)‘ATEP’(ENR-MOD.01.MPG)carried out within the framework of the Eurofusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No.633053。
文摘In this work,the gyrokinetic eigenvalue code LIGKA,the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes(RSAEs).Using the parameters from an ASDEXUpgrade plasma,a benchmark with the three different physical models for RSAE without and with energetic particles(EPs)is carried out.Reasonable agreement has been found for the mode frequency and the growth rate.Mode structure symmetry breaking(MSSB)is observed when EPs are included,due to the EPs’non-perturbative effects.It is found that the MSSB properties are featured by a finite radial wave phase velocity,and the linear mode structure can be well described by an analytical complex Gaussian expressionФ(s)=e^(-σ(s-s_(0))^(2))with complex parametersσand s_(0),where s is the normalized radial coordinate.The mode structure is distorted in opposite manners when the EP drive shifted from one side of qminto the other side,and specifically,a non-zero average radial wave number with opposite signs is generated.The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport.The parallel velocity of EPs is generated in opposite directions,due to different values of the average radial wave number,corresponding to different initial EP density profiles with EP drive shifted away from the qmin.
