This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin model...This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin models.DSR extends Einstein's special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies.In this context,we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra.These spectra are subsequently used to compute the partition function and key thermodynamic quantities,including specific heat,by employing the Euler-Maclaurin formula to facilitate an efficient approximation of the partition function.The analysis is restricted to the positive-energy sector,enabled by the exact Foldy-Wouthuysen transformation,which effectively decouples positive and negative energy states.The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework,thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.展开更多
The future space-borne gravitational wave(GW)detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions.The predictions for the GW background ...The future space-borne gravitational wave(GW)detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions.The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings,which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking(EWSB).In this paper,using the scalar N-plet model as a demonstration,we propose an effective classification for three different patterns of EWSB:(1)radiative symmetry breaking with classical scale invariance,(2)the Higgs mechanism in a generic scalar extension,and(3)higher-dimensional operators.We conclude that a strong first-order phase transition could be realized for(1)and(2)with a small quartic coupling and a small isospin of an additional N-plet field for the light scalar field model with and without the classical scale invariance,and(3)with a large mixing coupling between scalar fields and a large isospin of the N-plet field for the heavy scalar field model.展开更多
基金funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan,Program No.BR24992759。
文摘This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity(DSR):the Amelino-Camelia and Magueijo-Smolin models.DSR extends Einstein's special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies.In this context,we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra.These spectra are subsequently used to compute the partition function and key thermodynamic quantities,including specific heat,by employing the Euler-Maclaurin formula to facilitate an efficient approximation of the partition function.The analysis is restricted to the positive-energy sector,enabled by the exact Foldy-Wouthuysen transformation,which effectively decouples positive and negative energy states.The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework,thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.
基金supported by the National Key Research and Development Program of China under Grant Nos.2021YFC2203004,2021YFA0718304,2020YFC2201501RGC is supported by the National Natural Science Foundation of China under Grants Nos.11947302,11991052,11690022,11821505 and 11851302+8 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(CAS)under Grant Nos.XDB23030100 and XDA15020701the Key Research Program of the CAS under Grant No.XDPB15the Key Research Program of Frontier Sciences of CAS.SJW is supported by the National Key Research and Development Program of China under Grant Nos.2021YFC2203004 and 2021YFA0718304the National Natural Science Foundation of China under Grant Nos.12422502 and 12105344the China Manned Space Project under Grant No.CMS-CSST-2021-B01JHY is supported by the National Science Foundation of China under Grant Nos.12022514,11875003 and 12047503the National Key Research and Development Program of China under Grant Nos.2020YFC2201501 and 2021YFA0718304the CAS Project for Young Scientists in Basic Research under Grant No.YSBR-006the Key Research Program of the CAS under Grant No.XDPB15.
文摘The future space-borne gravitational wave(GW)detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions.The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings,which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking(EWSB).In this paper,using the scalar N-plet model as a demonstration,we propose an effective classification for three different patterns of EWSB:(1)radiative symmetry breaking with classical scale invariance,(2)the Higgs mechanism in a generic scalar extension,and(3)higher-dimensional operators.We conclude that a strong first-order phase transition could be realized for(1)and(2)with a small quartic coupling and a small isospin of an additional N-plet field for the light scalar field model with and without the classical scale invariance,and(3)with a large mixing coupling between scalar fields and a large isospin of the N-plet field for the heavy scalar field model.
