Related papers: Matrix computations for the dynamics of fermionic …
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
The recently introduced harmonic resolvent framework is concerned with the study of the input-output dynamics of nonlinear flows in the proximity of a known time-periodic orbit. These dynamics are governed by the harmonic resolvent…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
Using a map between the Lindbladian evolution of dephasing in free fermions and the time evolution of imaginary-interaction Fermi-Hubbard models in bipartite lattices, we present an efficient classical algorithm to solve the Schr\"{o}dinger…
We present a treatment of many-body Fermionic systems that facilitates an expression of the well-known quantities in a series expansion of the Planck's constant. The ensuing semiclassical result contains to a leading order of the response…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems,…
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not…
A Grassmann functional phase space is formulated for the definition of fermionic Wigner functionals by identifying suitable fermionic operators that are analogues to boson quadrature operators. Instead of the Majorana operators, we use…
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…