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We prove that conformal curved spacetime can be encoded into the initial wave function and that curved propagation can be simulated on a two-dimensional regular lattice with a finite set of homogeneous unitary operators. We generalize…
We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…
Derivation of the procedures that can be applied in evaluating two-time correlation function in terms of coherent-state propagator and corresponding Q-function is presented. On the basis that the involved functions are generally exponential…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating…
X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge invariant operators to be equal to their noninteracting values at particular…
In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose…
This is the second in a series of papers which considers first-order gauge-invariant and covariant gravitational perturbations to locally rotationally symmetric (LRS) class II space-times. This paper shows how to decouple a complex…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
The focus of this work is a correspondence between the Hilbert space operators on one hand, and doubly periodic generalized functions on the other. The linear map that implements it, referred to as the Q-transform, enables a direct…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…
We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
This paper is a sequence of the work presented in [1], where, the principles of the general relativity have been used to formulate quantum wave equations taking into account the effect of the electromagnetic and strong interactions in the…
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning…
As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation…