Related papers: On the Quantum Kinetic Equation in Weak Turbulence
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
The concept of weak invariants has recently been introduced in the context of conserved quantities in finite-time processes in nonequilibrium quantum thermodynamics. A weak invariant itself has a time-dependent spectrum, but its expectation…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
A user friendly scheme based on the quantum kinetic equation is developed for studying thermal transport phenomena in the presence of interactions and disorder. We demonstrate that this scheme is suitable for both a systematic perturbative…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
We define a new quantum Hermitian operator (namely, the energy variance operator) which is simply duplicated from the statistical definition of energy variance in classical physics. Its expectation value yields the standard deviation of the…
We propose to use the complex quantum dynamics of a massive particle in a non-quadratic potential to reconstruct an initial unknown motional quantum state. We theoretically show that the reconstruction can be efficiently done by measuring…
In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\half\mu^2x^2-\lambda x^4 in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C…
Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…