Related papers: Fermion Determinant Calculus
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…
Many manifestly non-Hermitian Hamiltonians (typically, PT-symmetric complex anharmonic oscillators) possess a strictly real, "physical" bound-state spectrum. This means that they are (quasi-)Hermitian with respect to a suitable non-standard…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
We introduce and solve a model of fermions hopping between neighbouring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the…
We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously.…
Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing…
We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval. In conventional studies this computation is…
The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…
We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $\omega_D$. These…
The response to a magnetic flux is considered of the vacuum state of charged Dirac fermions interacting with a domain wall made of a neutral spinless field in (3+1) dimensions with the fermion mass having a phase variation across the wall.…
The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…
In principle every excitation acquires a finite lifetime in a hot system. This nonzero spectral width is calculated self-consistently for massive fermions coupled to massless scalar, vector and pseudoscalar bosons. It is shown that the…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
The harmonic oscillator propagator is found straightforwardly from the free particle propagator, within the imaginary-time Feynman path integral formalism. The derivation presented here is extremely simple, requiring only elementary…
We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in (2+1) dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well…
We extend our previous study of Markov chains on finite commutative rings (arXiv:1605.05089) to arbitrary finite rings with identity. At each step, we either add or multiply by a randomly chosen element of the ring, where the addition…
Advance in quantum simulations using trapped ions or superconducting elements allows detailed analysis of the transverse field Ising model (TFIM), which can exhibit a quantum phase transition and has been a paradigm in exactly solvable…
Phase difference function is established by means of phase transfer function between time domains of source and interference point. The function reveals a necessary interrelation between outcome of two-beam interference, source's frequency…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…