Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space devel...Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.展开更多
There are two states of methane existing in coal, free methane and adsorptive methane. The two states of methane exchanged with each other which need the energy exchange with outside. It is released heat when methane ...There are two states of methane existing in coal, free methane and adsorptive methane. The two states of methane exchanged with each other which need the energy exchange with outside. It is released heat when methane adsorption on coal, instead of absorbed heat. According to the gas molecules Boltzmann energy distribution, is obtained the equilibrium equations of the two states of methane in coal, as well as the heat of adsorption equation when exchanged into each other. At the same time, high temperature experiments of methane adsorption on coal have been certificated to the theoretical model. At last the experimental results presented that： the two-state energy model could be accurately described the distribution of the two states of methane in the coal; the adsorption heat is related to the initial equilibrium state of methane adsorption; the adsorption heats are different with different coal ranks.展开更多
The model of double-well Bose-Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states ...The model of double-well Bose-Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states ｜N, 0〉 and [0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Foek states.展开更多
Large-signal modulation capability, as an important performance indicator, is directly related to the high-speed optical communication technology involved. We experimentally and theoretically investigate the large-sig...Large-signal modulation capability, as an important performance indicator, is directly related to the high-speed optical communication technology involved. We experimentally and theoretically investigate the large-signal modulation characteristics of the simultaneous ground-state （GS） and the excited-state （ES） lasing in InAs/OaAs quantum dot laser diodes. The large-signal modulation capability of total light intensity in the transition regime from OS lasing to two-state lasing is unchanged as the bias-current increases. However, GS and ES large-signal eye diagrams show obvious variations during the transition. Relaxation oscillations and large-signal eye diagrams for OS, ES, and total light intensities are numerically simulated and analyzed in detail by using a rate-equation model. The -ndings show that a complementary relationship between the light intensities for OS and ES lasing exists in both the transition regime and the two-state lasing regime, leading to a much smaller overshooting power and a shorter settling time for the total light intensity. Therefore, the eye diagrams of GS or ES lasing are diffuse whereas those of total light intensity are constant as the bias-current increases in the transition regime.展开更多
Air pollution is a significant problem in modern societies since it has a serious impact on human health and the environment.Particulate Matter(PM_(2.5))is a type of air pollution that contains of interrupted elements...Air pollution is a significant problem in modern societies since it has a serious impact on human health and the environment.Particulate Matter(PM_(2.5))is a type of air pollution that contains of interrupted elements with a diameter less than or equal to 2.5 m.For risk assessment and epidemiological investigations,a better knowledge of the spatiotemporal variation of PM_(2.5) concentration in a constant space-time area is essential.Conventional spatiotemporal interpolation approaches commonly relying on robust presumption by limiting interpolation algorithms to those with explicit and basic mathematical expression,ignoring a plethora of hidden but crucial manipulating aspects.Many advanced deep learning approaches have been proposed to forecast Particulate Matter(PM_(2.5)).Recurrent neural network(RNN)is one of the popular deep learning architectures which is widely employed in PM_(2.5) concentration forecasting.In this research,we proposed a Two-State Gated Recurrent Unit(TS-GRU)for monitoring and estimating the PM_(2.5) concentration forecasting system.The proposed algorithm is capable of considering both spatial and temporal hidden affecting elements spontaneously.We tested our model using data from daily PM_(2.5) dimensions taken in the contactual southeast area of the United States in 2009.In the studies,three evaluation matrices were utilized to compare the overall performance of each algorithm:Mean Absolute Error(MAE),Root Mean Square Error(RMSE),and Mean Absolute Percentage Error(MAPE).The experimental results revealed that our proposed TS-GRU model outperformed compared to the other deep learning approaches in terms of forecasting performance.展开更多
In the famous EPR paper published in 1935, Einstein, Podolsky, and Rosen suggested a thought experiment, which later became known as the “EPR experiment”. Using the EPR experiment, they posited that quantum mechanic...In the famous EPR paper published in 1935, Einstein, Podolsky, and Rosen suggested a thought experiment, which later became known as the “EPR experiment”. Using the EPR experiment, they posited that quantum mechanics was incomplete. Einstein, however, was dissatisfied with the EPR paper and published a second work on the EPR experiment, in which he discussed the dilemma of choosing whether quantum mechanics was incomplete or nonlocal. Currently, most physicists choose the nonlocality of quantum mechanics over Einstein’s choice of the incompleteness of quantum mechanics. However, with an appropriate alternate hypothesis, both of these choices can be rejected. Herein, I demonstrate an approach to overcome the Einstein Dilemma by proposing a new interpretation invoked by a new formalism of quantum mechanics known as two-state vector formalism.展开更多
In this paper, I show that an interpretation of quantum mechanics using two-state vector formalism proposed by Aharonov, Bergmann, and Lebowitz, can solve one of the measurement problems formulated by Maudlin. Accordi...In this paper, I show that an interpretation of quantum mechanics using two-state vector formalism proposed by Aharonov, Bergmann, and Lebowitz, can solve one of the measurement problems formulated by Maudlin. According to this interpretation, we can simultaneously insist that the wave function of a system is complete, that the wave function is determined by the Schr?dinger equation, and that the measurement of a physical quantity always has determinate outcomes, although Maudlin in his formulation of the measurement problem states that these three claims are mutually inconsistent. Further, I show that my interpretation does not contradict the uncertainty relation and the no-go theorem.展开更多
The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while fo...The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.展开更多
Gas-phase CO_2 catalyzed activation hydrogenation by Ru atoms was studied with density functional theory. Based on the structure optimization of different potential energy surfaces,there are two crossing points betwee...Gas-phase CO_2 catalyzed activation hydrogenation by Ru atoms was studied with density functional theory. Based on the structure optimization of different potential energy surfaces,there are two crossing points between singlet and triplet potential energy surfaces and there is a crossing point between quintet and triplet potential energy surfaces in the whole catalytic cycle. Spin transition probabilities in the vicinity of the intersections have been calculated by the Landau-Zener model theory. There are three minimum energy crossing points（MECPs） with strong spin-orbital coupling effect and higher spin transition probability,and all spin inversion occurred in s orbital and different d orbitals of ruthenium,indicating this is a typical two-state reactivity（TSR） reaction. Finally,the lowest energy reaction path is ensured.展开更多
The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model ...The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model is carefully examined by comparing the harmonic spectra of hydrogen molecular ion obtained from this model with those from the three-dimensional time-dependent Schr¨odinger equation. When combined with the Morlet transform of quantum time-frequency spectrum,the two-state model can be used to study the dynamical origin of the low-order harmonic generation of hydrogen molecular ion driven by low-frequency pulses. In addition, some interesting structures of the time profiles for low order harmonics are obtained.展开更多
The two-state mechanism of the reaction of Nb(NH2)3 with N2O on the singlet and triplet potential energy surfaces has been investigated at the B3LYP level.Crossing points between the potential energy surfaces have bee...The two-state mechanism of the reaction of Nb(NH2)3 with N2O on the singlet and triplet potential energy surfaces has been investigated at the B3LYP level.Crossing points between the potential energy surfaces have been located using different methods.Analysis of the strain model shows that the singlet state of the four-coordinate(N2O)Nb(NH2)3 complex with N2O bonded via terminal N atom coordination(12) is more stable in the initial stage of reaction,since the bending of the N2O fragment [Edef(N2O) = 86.1 kcal mol-1] results in an energy splitting of the doubly degenerate LUMO;the low-energy LUMO can now strongly couple with the occupied Nb-localized d orbitals,forming a back-bond and transferring charge(q = 0.82 e) from Nb(NH2)3 to the N2O ligand.Going from 32 to 12,the reacting system changes spin multiplicity near the MECP(minimal energy crossing point) region,which takes place with a spin crossing barrier of 9.6-10.0 kcal mol-1.Analysis of spin-orbit coupling(SOC) indicates that MECP will produce a significant SOC matrix element.The value of SOC is 111.52 cm-1,due to the electron shift between two perpendicular φ orbitals with the same rotation direction,and the magnitude of the spin-multi-plicity mixing increases in the small energy gap between high-and low-spin states,greatly enhancing the probability of intersystem crossing.The probabilities of single(P1 ISC) and double(P2 ISC) passes estimated at MECP(SOC = 111.52 cm-1) are approximately 1.17×10-2 and 2.32×10-2,respectively.展开更多
The two-state reaction mechanism of CpCo(C_4H_4)with isocyanate on the triplet and singlet potential energy surfaces has been investigated at the B3LYP level.A study is described for the computation of spin-orbit coup...The two-state reaction mechanism of CpCo(C_4H_4)with isocyanate on the triplet and singlet potential energy surfaces has been investigated at the B3LYP level.A study is described for the computation of spin-orbit coupling of triplet state of the minimal energy crossing point(CP)with their singlet states and of the zerofield splitting(ZFS)parameters of the triplet states,including the full one-and two-electron terms of the BreitPauli Hamiltonian.There are two key crossing points along this two-state reaction pathway.The first crossing point—CP2 exists near^1B.The reacting system will change its spin multiplicity from the triplet state to the singlet state near this crossing region.Although the spin-orbit coupling interaction and ZFS D-tensor of the CP2 region are very strong,the reaction system will occur the reverse intersystem crossing from T_1 to S_0.Therefore,its spin-flip efficiency may be lower.The second crossing point,CP3will again change its spin multiplicity from the singlet state to the triplet state in the Co-Cr bond activation pathway,leading to a decrease in the barrier height of^1TS(CF)from19.5 to 9.5 kcal/mol(1cal=4.182 J),and the efficiency of intersystem crossing from S_0 to T_1 is high because the larger spin-orbit coupling(SOC)matrix elements will result in the overpopulations of the three sublevels of T_1(3.30×10^(-1),3.32×10^(-1),and 3.38×10^(-1),respectively).展开更多
文摘Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.
基金Supported by the National Natural Science Foundation of China （21373146）
文摘There are two states of methane existing in coal, free methane and adsorptive methane. The two states of methane exchanged with each other which need the energy exchange with outside. It is released heat when methane adsorption on coal, instead of absorbed heat. According to the gas molecules Boltzmann energy distribution, is obtained the equilibrium equations of the two states of methane in coal, as well as the heat of adsorption equation when exchanged into each other. At the same time, high temperature experiments of methane adsorption on coal have been certificated to the theoretical model. At last the experimental results presented that： the two-state energy model could be accurately described the distribution of the two states of methane in the coal; the adsorption heat is related to the initial equilibrium state of methane adsorption; the adsorption heats are different with different coal ranks.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos.60478029,10575040,10634060,and 90503010the National Fundamental Research Program of China under Grant No.2005CB724508
文摘The model of double-well Bose-Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states ｜N, 0〉 and [0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Foek states.
基金Supported by the National Key Research and Development Program of China under Grant No 2016YFB0402302the National Natural Science Foundation of China under Grant No 91433206
文摘Large-signal modulation capability, as an important performance indicator, is directly related to the high-speed optical communication technology involved. We experimentally and theoretically investigate the large-signal modulation characteristics of the simultaneous ground-state （GS） and the excited-state （ES） lasing in InAs/OaAs quantum dot laser diodes. The large-signal modulation capability of total light intensity in the transition regime from OS lasing to two-state lasing is unchanged as the bias-current increases. However, GS and ES large-signal eye diagrams show obvious variations during the transition. Relaxation oscillations and large-signal eye diagrams for OS, ES, and total light intensities are numerically simulated and analyzed in detail by using a rate-equation model. The -ndings show that a complementary relationship between the light intensities for OS and ES lasing exists in both the transition regime and the two-state lasing regime, leading to a much smaller overshooting power and a shorter settling time for the total light intensity. Therefore, the eye diagrams of GS or ES lasing are diffuse whereas those of total light intensity are constant as the bias-current increases in the transition regime.
基金This research work supported by Khalid University of Saudi Arabia under the grant number R.G.P.1/365/42.
文摘Air pollution is a significant problem in modern societies since it has a serious impact on human health and the environment.Particulate Matter(PM_(2.5))is a type of air pollution that contains of interrupted elements with a diameter less than or equal to 2.5 m.For risk assessment and epidemiological investigations,a better knowledge of the spatiotemporal variation of PM_(2.5) concentration in a constant space-time area is essential.Conventional spatiotemporal interpolation approaches commonly relying on robust presumption by limiting interpolation algorithms to those with explicit and basic mathematical expression,ignoring a plethora of hidden but crucial manipulating aspects.Many advanced deep learning approaches have been proposed to forecast Particulate Matter(PM_(2.5)).Recurrent neural network(RNN)is one of the popular deep learning architectures which is widely employed in PM_(2.5) concentration forecasting.In this research,we proposed a Two-State Gated Recurrent Unit(TS-GRU)for monitoring and estimating the PM_(2.5) concentration forecasting system.The proposed algorithm is capable of considering both spatial and temporal hidden affecting elements spontaneously.We tested our model using data from daily PM_(2.5) dimensions taken in the contactual southeast area of the United States in 2009.In the studies,three evaluation matrices were utilized to compare the overall performance of each algorithm:Mean Absolute Error(MAE),Root Mean Square Error(RMSE),and Mean Absolute Percentage Error(MAPE).The experimental results revealed that our proposed TS-GRU model outperformed compared to the other deep learning approaches in terms of forecasting performance.
文摘In the famous EPR paper published in 1935, Einstein, Podolsky, and Rosen suggested a thought experiment, which later became known as the “EPR experiment”. Using the EPR experiment, they posited that quantum mechanics was incomplete. Einstein, however, was dissatisfied with the EPR paper and published a second work on the EPR experiment, in which he discussed the dilemma of choosing whether quantum mechanics was incomplete or nonlocal. Currently, most physicists choose the nonlocality of quantum mechanics over Einstein’s choice of the incompleteness of quantum mechanics. However, with an appropriate alternate hypothesis, both of these choices can be rejected. Herein, I demonstrate an approach to overcome the Einstein Dilemma by proposing a new interpretation invoked by a new formalism of quantum mechanics known as two-state vector formalism.
文摘In this paper, I show that an interpretation of quantum mechanics using two-state vector formalism proposed by Aharonov, Bergmann, and Lebowitz, can solve one of the measurement problems formulated by Maudlin. According to this interpretation, we can simultaneously insist that the wave function of a system is complete, that the wave function is determined by the Schr?dinger equation, and that the measurement of a physical quantity always has determinate outcomes, although Maudlin in his formulation of the measurement problem states that these three claims are mutually inconsistent. Further, I show that my interpretation does not contradict the uncertainty relation and the no-go theorem.
文摘The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.
基金supported by the National Natural Science Foundation of China(21263023)
文摘Gas-phase CO_2 catalyzed activation hydrogenation by Ru atoms was studied with density functional theory. Based on the structure optimization of different potential energy surfaces,there are two crossing points between singlet and triplet potential energy surfaces and there is a crossing point between quintet and triplet potential energy surfaces in the whole catalytic cycle. Spin transition probabilities in the vicinity of the intersections have been calculated by the Landau-Zener model theory. There are three minimum energy crossing points（MECPs） with strong spin-orbital coupling effect and higher spin transition probability,and all spin inversion occurred in s orbital and different d orbitals of ruthenium,indicating this is a typical two-state reactivity（TSR） reaction. Finally,the lowest energy reaction path is ensured.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11465016,11674268,and 11764038)
文摘The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model is carefully examined by comparing the harmonic spectra of hydrogen molecular ion obtained from this model with those from the three-dimensional time-dependent Schr¨odinger equation. When combined with the Morlet transform of quantum time-frequency spectrum,the two-state model can be used to study the dynamical origin of the low-order harmonic generation of hydrogen molecular ion driven by low-frequency pulses. In addition, some interesting structures of the time profiles for low order harmonics are obtained.
基金Tianshui Normal University for a grant from the "QingLan" Talent Engineering Fundsthe Key Project of Chinese Ministry of Education(211189) for support of this research
文摘The two-state mechanism of the reaction of Nb(NH2)3 with N2O on the singlet and triplet potential energy surfaces has been investigated at the B3LYP level.Crossing points between the potential energy surfaces have been located using different methods.Analysis of the strain model shows that the singlet state of the four-coordinate(N2O)Nb(NH2)3 complex with N2O bonded via terminal N atom coordination(12) is more stable in the initial stage of reaction,since the bending of the N2O fragment [Edef(N2O) = 86.1 kcal mol-1] results in an energy splitting of the doubly degenerate LUMO;the low-energy LUMO can now strongly couple with the occupied Nb-localized d orbitals,forming a back-bond and transferring charge(q = 0.82 e) from Nb(NH2)3 to the N2O ligand.Going from 32 to 12,the reacting system changes spin multiplicity near the MECP(minimal energy crossing point) region,which takes place with a spin crossing barrier of 9.6-10.0 kcal mol-1.Analysis of spin-orbit coupling(SOC) indicates that MECP will produce a significant SOC matrix element.The value of SOC is 111.52 cm-1,due to the electron shift between two perpendicular φ orbitals with the same rotation direction,and the magnitude of the spin-multi-plicity mixing increases in the small energy gap between high-and low-spin states,greatly enhancing the probability of intersystem crossing.The probabilities of single(P1 ISC) and double(P2 ISC) passes estimated at MECP(SOC = 111.52 cm-1) are approximately 1.17×10-2 and 2.32×10-2,respectively.
基金supported by the National Natural Science Foundation of China(21263022)University Research Fund of Gansu Province Financial Department,and"QingLan"Talent Engineering Funds of Tianshui Normal University
文摘The two-state reaction mechanism of CpCo(C_4H_4)with isocyanate on the triplet and singlet potential energy surfaces has been investigated at the B3LYP level.A study is described for the computation of spin-orbit coupling of triplet state of the minimal energy crossing point(CP)with their singlet states and of the zerofield splitting(ZFS)parameters of the triplet states,including the full one-and two-electron terms of the BreitPauli Hamiltonian.There are two key crossing points along this two-state reaction pathway.The first crossing point—CP2 exists near^1B.The reacting system will change its spin multiplicity from the triplet state to the singlet state near this crossing region.Although the spin-orbit coupling interaction and ZFS D-tensor of the CP2 region are very strong,the reaction system will occur the reverse intersystem crossing from T_1 to S_0.Therefore,its spin-flip efficiency may be lower.The second crossing point,CP3will again change its spin multiplicity from the singlet state to the triplet state in the Co-Cr bond activation pathway,leading to a decrease in the barrier height of^1TS(CF)from19.5 to 9.5 kcal/mol(1cal=4.182 J),and the efficiency of intersystem crossing from S_0 to T_1 is high because the larger spin-orbit coupling(SOC)matrix elements will result in the overpopulations of the three sublevels of T_1(3.30×10^(-1),3.32×10^(-1),and 3.38×10^(-1),respectively).
