相关论文: Recursive approach to supersymmetric quantum mecha…

We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…

We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its…

Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…

We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…

The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional…

We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lema\^{i}tre-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus…

It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…

We propose a numerical method of estimating various physical quantities in lattice (supersymmetric) quantum mechanics. The method consists only of deterministic processes such as computing a product of transfer matrix, and has no…

We present a quantum algorithm to compute the logarithm of the determinant of the fermion matrix, assuming access to a classical lattice gauge field configuration. The algorithm uses the quantum eigenvalue transform, and quantum mean…

I present here a new method that allows the introduction of a discrete auxiliary symmetry in a theory in such a way that the eigenvalue spectrum of the fermion functional determinant is made up of complex conjugated pairs. The method…

This is a brief survey of applications of the harmonic superspace methods to the models of N=4 supersymmetric quantum mechanics (SQM). The main focus is on a recent progress in constructing SQM models with couplings to the background…

Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single…

We present a detailed Hamiltonian treatment of an inhomogeneous fermionic perturbation propagating on a closed FLRW spacetime quantized via LQC. Expanding the fermion in spinor harmonics on spatial 3-sphere and truncating at quadratic…

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…

A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…

We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence…

The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a…

Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus…