There are rich emergent phase behaviors in non-equilibrium active systems.Flocking and clustering are two representative dynamic phases.The relationship between both the phases is still unclear.Herein,we numerically i...There are rich emergent phase behaviors in non-equilibrium active systems.Flocking and clustering are two representative dynamic phases.The relationship between both the phases is still unclear.Herein,we numerically investigate the evolution of flocking and clustering in a system consisting of self-propelled particles with active reorientation.We consider the interplay between flocking and clustering phases with different initial configurations,and observe a domain in steady state order parameter phase diagrams sensitive to the choice of initial configurations.Specifically,by tuning the initial degree of polar ordering,either a more ordered flocking or a disordered clustering state can be observed in the steady state.These results enlighten us to manipulate emergent behaviors and collective motions of an active system,and are qualitatively different from the emergence of a new bi-stable regime observed in aligned active particles due to an explicit attraction[New J.Phys.14073033(2012)].展开更多
The Carnot-like heat engines are classified into three types （normal-, sub- and, super-dissipative） accord- ing to relations between the minimum irreversible entropy production in the ＂isothermal＂ processes and th...The Carnot-like heat engines are classified into three types （normal-, sub- and, super-dissipative） accord- ing to relations between the minimum irreversible entropy production in the ＂isothermal＂ processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between ηc/2 and ηc/ （2 - ηc ）, ηc /2 and ηc, 0 and ηc/ （2 - ηc ）, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Left. 98 （2012） 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.展开更多
Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantu...Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements.We demonstrate that convolutional neural network(CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states(or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.展开更多
This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ah...This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman＇s ratchet as a heat engine are presented. It is found that： the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.展开更多
Neural networks have provided powerful approaches to solve various scientific problems.Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data.We investigat...Neural networks have provided powerful approaches to solve various scientific problems.Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data.We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion.Firstly,we predict the orbits of planets in the geocentric system using the gate recurrent unit,one of the common neural networks.We find that the precision of the prediction is obviously improved when the information of the Sun is included in the training set.This result implies that the Sun is particularly important in the geocentric system without any prior knowledge,which inspires us to gain Copernicus'heliocentric theory.Secondly,we turn to the heliocentric system and make successfully mutual predictions between the position and velocity of planets.We hold that the successful prediction is due to the existence of enough conserved quantities(such as conservations of mechanical energy and angular momentum)in the system.Our research provides a new way to explore the existence of conserved quantities in mechanics system based on neural networks.展开更多
The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom′as et al., Phys. Rev. E 85(2012) 010104(R)]. The χ-criterion for Fe...The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom′as et al., Phys. Rev. E 85(2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.展开更多
We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field,which involve（i）the exact solutions to the shape equation of lipid vesic...We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field,which involve（i）the exact solutions to the shape equation of lipid vesicles,（ii）the exact solutions to the governing equations of open lipid membranes,（iii）the neck condition of two-phase vesicles in the budding state,（iv） the nonlocal theory of membrane elasticity,and（v）the relationship between the symmetry and the magnitude of the free energy.展开更多
The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related ...The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated.An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived,which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose–Einstein condensates.It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior.For stable dynamics,some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously,which is consistent with the derivative relation.展开更多
The shape equation of lipid membranes is a fourth-order partial differential equation.Under the axisymmetric condi-tion,this equation was transformed into a second-order ordinary differential equation(ODE)by Zheng and...The shape equation of lipid membranes is a fourth-order partial differential equation.Under the axisymmetric condi-tion,this equation was transformed into a second-order ordinary differential equation(ODE)by Zheng and Liu(Phys.Rev.E 482856(1993)).Here we try to further reduce this second-order ODE to a first-order ODE.First,we invert the usual process of variational calculus,that is,we construct a Lagrangian for which the ODE is the corresponding Euler-Lagrange equation.Then,we seek symmetries of this Lagrangian according to the Noether theorem.Under a certain restriction on Lie groups of the shape equation,we find that the first integral only exists when the shape equation is identical to the Will-more equation,in which case the symmetry leading to the first integral is scale invariance.We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor.展开更多
基金support from the Beijing Computational Science Research Centersupported by the National Natural Science Foundation of China(Grant Nos.U2230402,11975050,11735005,and 11904320)。
文摘There are rich emergent phase behaviors in non-equilibrium active systems.Flocking and clustering are two representative dynamic phases.The relationship between both the phases is still unclear.Herein,we numerically investigate the evolution of flocking and clustering in a system consisting of self-propelled particles with active reorientation.We consider the interplay between flocking and clustering phases with different initial configurations,and observe a domain in steady state order parameter phase diagrams sensitive to the choice of initial configurations.Specifically,by tuning the initial degree of polar ordering,either a more ordered flocking or a disordered clustering state can be observed in the steady state.These results enlighten us to manipulate emergent behaviors and collective motions of an active system,and are qualitatively different from the emergence of a new bi-stable regime observed in aligned active particles due to an explicit attraction[New J.Phys.14073033(2012)].
基金Supported by the National Natural Science Foundation of China under Grant No. 11075015the Fundamental Research Funds for the Central Universities
文摘The Carnot-like heat engines are classified into three types （normal-, sub- and, super-dissipative） accord- ing to relations between the minimum irreversible entropy production in the ＂isothermal＂ processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between ηc/2 and ηc/ （2 - ηc ）, ηc /2 and ηc, 0 and ηc/ （2 - ηc ）, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Left. 98 （2012） 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 12004266, 11834014 and 11975050)the Beijing Natural Science Foundation (Grant Nos. 1192005 and Z180013)+1 种基金the Foundation of Beijing Education Committees (Grant No.KM202010028013)the Academy for Multidisciplinary Studies,Capital Normal University。
文摘Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements.We demonstrate that convolutional neural network(CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states(or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.
基金supported by the National Natural Science Foundation of China (Grant No.11075015)the Fundamental Research Funds for the Central Universities
文摘This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman＇s ratchet as a heat engine are presented. It is found that： the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975050).
文摘Neural networks have provided powerful approaches to solve various scientific problems.Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data.We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion.Firstly,we predict the orbits of planets in the geocentric system using the gate recurrent unit,one of the common neural networks.We find that the precision of the prediction is obviously improved when the information of the Sun is included in the training set.This result implies that the Sun is particularly important in the geocentric system without any prior knowledge,which inspires us to gain Copernicus'heliocentric theory.Secondly,we turn to the heliocentric system and make successfully mutual predictions between the position and velocity of planets.We hold that the successful prediction is due to the existence of enough conserved quantities(such as conservations of mechanical energy and angular momentum)in the system.Our research provides a new way to explore the existence of conserved quantities in mechanics system based on neural networks.
基金Supported by National Natural Science Foundation of China under Grant No.11322543
文摘The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom′as et al., Phys. Rev. E 85(2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11274046)
文摘We report some key results in the theoretical investigations of configurations of lipid membranes and present several challenges in this field,which involve（i）the exact solutions to the shape equation of lipid vesicles,（ii）the exact solutions to the governing equations of open lipid membranes,（iii）the neck condition of two-phase vesicles in the budding state,（iv） the nonlocal theory of membrane elasticity,and（v）the relationship between the symmetry and the magnitude of the free energy.
基金financial support from the National Natural Science Foundation of China(Grants No.11675017 and No.11975050)。
文摘The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated.An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived,which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose–Einstein condensates.It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior.For stable dynamics,some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously,which is consistent with the derivative relation.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274046)the National Science Foundation of the United States(Grant No.1515007)
文摘The shape equation of lipid membranes is a fourth-order partial differential equation.Under the axisymmetric condi-tion,this equation was transformed into a second-order ordinary differential equation(ODE)by Zheng and Liu(Phys.Rev.E 482856(1993)).Here we try to further reduce this second-order ODE to a first-order ODE.First,we invert the usual process of variational calculus,that is,we construct a Lagrangian for which the ODE is the corresponding Euler-Lagrange equation.Then,we seek symmetries of this Lagrangian according to the Noether theorem.Under a certain restriction on Lie groups of the shape equation,we find that the first integral only exists when the shape equation is identical to the Will-more equation,in which case the symmetry leading to the first integral is scale invariance.We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor.
