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A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a…
For some time the York time parameter has been identified as a candidate for a physically meaningful time in cosmology. An associated Hamiltonian may be found by solving the Hamiltonian constraint for the momentum conjugate to the York time…
The Fluctuation Theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy…
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…
We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
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…
Finding the consequences of symmetry for open system quantum dynamics is a problem with broad applications, including describing thermal relaxation, deriving quantum limits on the performance of amplifiers, and exploring quantum metrology…