The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kern...The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kernel or generator, which describes eflhcts of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion （HEOM） and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with diflhrent sets of parameters, to investigate the convergence of the high order expansiolls of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.展开更多
There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle th...There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.展开更多
In fitting the double-differential measurements thelevelwidth broadening effect should be taken into account properly due to Heisenberg uncertainty.Besides level width broadening effect the energy resolution in the me...In fitting the double-differential measurements thelevelwidth broadening effect should be taken into account properly due to Heisenberg uncertainty.Besides level width broadening effect the energy resolution in the measurements is also needed in this procedure.In general,the traditional normal Gaussian expansion is employed.However,the research indicates that to do so in this way the energy balance could not hold.For this reason,the deformed Gaussian expansion functions with exponential form for both the single energy point and continuous spectrum are introduced,with which the normalization and energy balance conditions could hold exactly in the analytical form.展开更多
The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms...The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms of Cauchy-type integrals;these expressions are natural generalizations of integral representations of the coe?cients and the remainders in the Taylor expansions of analytic functions.By using the new representation,a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived.展开更多
基金supported by the National Natural Science Foundation of China(No.21673246)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB12020300)
文摘The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kernel or generator, which describes eflhcts of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion （HEOM） and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with diflhrent sets of parameters, to investigate the convergence of the high order expansiolls of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.
文摘There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.
文摘In fitting the double-differential measurements thelevelwidth broadening effect should be taken into account properly due to Heisenberg uncertainty.Besides level width broadening effect the energy resolution in the measurements is also needed in this procedure.In general,the traditional normal Gaussian expansion is employed.However,the research indicates that to do so in this way the energy balance could not hold.For this reason,the deformed Gaussian expansion functions with exponential form for both the single energy point and continuous spectrum are introduced,with which the normalization and energy balance conditions could hold exactly in the analytical form.
文摘The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms of Cauchy-type integrals;these expressions are natural generalizations of integral representations of the coe?cients and the remainders in the Taylor expansions of analytic functions.By using the new representation,a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived.
