Related papers: Study of classical mechanical systems with complex…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
We study a reflectionless PT-symmetric quantum system described by the pair of complexified Scarf II potentials mutually displaced in the half of their pure imaginary period. Analyzing the rich set of intertwining discrete symmetries of the…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
The completeness of some classical statistical mechanical (SM) models is a recent result that has been developed by quantum formalism for the partition functions. In this paper, we consider a 2D classical $\phi^4$ filed theory whose…
Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate…
This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
A reflection-asymmetric deformed oscillator potential is analysed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the ''removal of…
Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many…
A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…
Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
Entangled quantum mechanical states in one dimension can be used to represent and simulate classical stochastic processes with nontrivial statistical properties. Long-range quantum correlations translate into fractional processes with their…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
The exact factorization of the time-dependent electron-nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating light-induced ultrafast processes. In this…