相关论文: Perturbative power series for block diagonalisatio…
We investigate quantum dynamics with the underlying Hamiltonian being a Jacobi or a block Jacobi matrix with the diagonal and the off-diagonal terms modulated by a periodic or a limit-periodic sequence. In particular, we investigate the…
In this paper we prove that there exists an asymptotical diagonalization algorithm for a class of sparse Hermitian (or real symmetric) matrices if and only if the matrices become Hessenberg matrices after some permutation of rows and…
Quantum logic decomposition refers to decomposing a given quantum gate to a set of physically implementable gates. An approach has been presented to decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation gates around z…
In effective models of loop quantum gravity, the onset of quantum effects is controlled by a so-called polymerisation scale. It is sometimes necessary to make this scale phase space dependent in order to obtain sensible physics. A…
This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit…
Physical nature of dimensional crossovers in weakly coupled Hubbard chains and ladders has been discussed within the framework of the perturbative renormalization-group approach. The difference between these two cases originates from…
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some…
In some instances of study of quantum evolution of classical backgrounds it is considered inevitable to resort to non-perturbative methods at the price of treating the system semiclassically. We show that a fully quantum perturbative…
We develop a theory of random non-Hermitian action that, after quantization, describes the stochastic nonlinear dynamics of quantum states in Hilbert space. Focusing on fermionic fields, we propose both canonical quantization and path…
We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic…
Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical definitions--via power series, spectral calculus, or Jordan…
Among all of the non-Hermitian large-tridiagonal-matrix quantum Hamiltonians we choose a subclass with the structure resembling the ``benchmark'' realistic Bose-Hubbard model. We demonstrate that this choice can be declared user-friendly in…
The wave-particle duality and its probabilistic interpretation are at the heart of quantum mechanics. Here we show that, in some standard contexts like the double slit experiment, a deterministic interpretation can be provided. This…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure…
We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above…
The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external…
We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level,…
When electron correlations are important it is often necessary to use numerical methods to solve the Hamiltonian for a finite system (cluster) "exactly". Unfortunately, such methods are restricted to small systems. We propose to combine the…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…