Related papers: The Feynman-Kac formula in deformation quantizatio…
This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications, phase space forms, master equation and liouville equation…
Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space…
The energy gap is calculated for the ground state quantum computer circuit, which was recently proposed by Mizel et.al. When implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
We study some examples of complex, classical, scalar fields within the new framework that we introduced in a previous work. In these particular examples, we replace the usual functional integral by a complex functional arising from partial…
The deformation star product of smooth functions on the momentum phase space of covariant (polysymplectic) Hamiltonian field theory is introduced.
We present a comprehensive quantum many body theory for kq deformed particles, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles…
We consider the renormalized relativistic Nelson model in two spatial dimensions for a finite number of spinless, relativistic quantum mechanical matter particles in interaction with a massive scalar quantized radiation field. We find a…
The ground-state energy, the addition energies and the optical absorption spectra are derived for interacting polarons in parabolic quantum dots in three and two dimensions. A path integral formalism for identical particles is used in order…
Quantum chemistry calculations are important applications of quantum annealing. For practical applications in quantum chemistry, it is essential to estimate a ground state energy of the Hamiltonian with chemical accuracy. However, there are…
We introduce reinforcement learning (RL) formulations of the problem of finding the ground state of a many-body quantum mechanical model defined on a lattice. We show that stoquastic Hamiltonians - those without a sign problem - have a…
The ground state energy of a quantum field in the background of classical field configurations is considered. The subject of the ground state energy in framework of the quantum field theory is explained. The short review of calculation…
We consider a Hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons. We show that the ground state projection and the ground state energy are…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
We consider the quantization of a scalar kappa-deformed field up to the point of obtaining an expression for its vacuum energy. The expression is given by the half sum of the field frequencies, as in the non-deformed case, but with the…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…