Related papers: Exact quantum statistics for electronically nonadi…
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and…
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and…
An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem.…
We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-1/2 coherent state, we…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian…
In the present work we introduce a computational approach to the absolute rovibrational quantum partition function using the path-integral formalism of quantum mechanics in combination with the nested sampling technique. The numerical…
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion…
This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very…
The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even…
We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…
Accurate and efficient simulation of nonadiabatic dynamics is highly desirable for understanding charge and energy transfer in complex systems. A key criterion for obtaining an accurate method is conservation of the Quantum Boltzmann…
Imaginary-time path integral (PI) is a rigorous tool to compute static properties at finite temperatures. However, the stiff PI internal modes poses a sampling challenge. This is commonly tackled using staging coordinates, in which the free…
On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme…
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…
We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson…
In the path integral formulation of the partition function of quantum spin models, most current treatments employ the so-called static approximation to simplify the process of summing over all possible paths. Although sufficient for…
We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…
We have developed a numerically exact approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…
We present two multistate ring polymer instanton (RPI) formulations, both obtained from an exact path integral representation of the quantum canonical partition function for multistate systems. The two RPIs differ in their treatment of the…