Related papers: Timescales for dynamical relaxation to the Born ru…
Bloch-Redfield equation is a common tool for studying evolution of qubit systems weakly coupled to environment. We investigate the accuracy of the Born approximation underlying this equation. We find that the high order terms in the…
We construct a generalization of the JIMWLK Hamiltonian, going beyond the eikonal approximation, which governs the high-energy evolution of the scattering between a dilute projectile and a dense target with an arbitrary longitudinal extent…
Using the prescription of the nonequilibrium statistical operator method, we derive a non-Markovian generalization to the kinetic theory described by Walser {\sl et al.} [Phys. Rev. A {\bf 59}, 3878 (1999)]. Quasi-particle damping and…
We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie-Bohm (deBB) theory: its reliance on the quantum probability formula to justify the…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
In this research we study the effect of matter-wave instability on electron beam transport with arbitrary degree of degeneracy. Particular class of solutions of the Schr\"{o}dinger-Poisson system is used to model the electron-beam transport…
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical…
We extend to nonequilibrium processes our recent theory for the long time dynamics of flexible chain molecules. While the previous theory describes the equilibrium motions for any bond or interatomic separation in (bio)polymers by time…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
Complex quantum trajectories, which were first obtained from a modified de Broglie-Bohm quantum mechanics, demonstrate that Born's probability axiom in quantum mechanics originates from dynamics itself. We show that a normalisable…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space. This choice is equivalent to the hypothesis of the discreteness of the…
Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…
Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum…
Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…
This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We…
The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle…
The Schr\"odinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the…