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Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
Complex, non-Hermitian potentials V(x) can often generate standard quantum bound states. H. F. Jones [Phys. Rev. D 78, 065032 (2008)] demonstrated that the idea cannot directly be transferred to scattering. We reveal that a return to the…
Calculations of high-energy processes involving the production of a large number of particles in weakly-coupled quantum field theories have previously signaled the need for novel non-perturbative behavior or even new physical phenomena. In…
It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that…
The energy spectra of mesoscopic, i.e. few-body quantum systems are of great interest in several areas of physics such as nuclear physics, cluster physics or magnetism. One way to obtain an approximate spectrum is to diagonalize with…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed…
In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…
A many-particle theory is presented for the effective quasistatic permittivity of macroscopically homogeneous and isotropic systems of inhomogeneous dielectric particles with different degrees of penetrability. The theory is based upon our…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
A simple relativistic quantum hidden-variable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum…
The amplitude of localized quantum states in random or disordered media may exhibit long range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these…
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy…
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…
We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation…
We find theoretical results on energy eigenvalues and corresponding supersymmetric Hamiltonians reflect contradictory behavior for negative values of A. furthermore the resulting supersymmetric partners potentials can be model scattering…
Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…
In this work we propose a many-body Hamiltonian construction which introduces only a single separate energy scale of order $\Theta(1/N^{2+\delta})$, for a small parameter $\delta>0$, and for $N$ terms in the target Hamiltonian. In its…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…