Related papers: An exact mapping between the states of arbitrary N…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schroedinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
Quantum many body system in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, nonequilibrium behaviour of quantum many body systems remains elusive, out of the range of such a well…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…
We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical…
We compute numerically the time evolution of simple semiclassical states describing homogeneous and isotropic spatial geometries in quantum-reduced loop gravity under a deparametrized formulation of the dynamics, in which a reference matter…
Three-dimensional N-vector spin models may define universality classes for such diverse phenomena as i) the superfluid transition in liquid helium (currently investigated in the micro-gravity environment of the Space Shuttle) and ii) the…
A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stuckelberg-Majorana (LZSM) interferometry, latching modulation, and motional averaging,…
We show that when a quantum system is coupled to an environment in a mean field way, then its effective dynamics is governed by a unitary group with a time-dependent Hamiltonian. The time-dependent modification of the bare system…
The complex geometry underlying the Schr\"odinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…