Related papers: Wiener-Type Theorems for the Laplace Transform. Wi…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
We analyse a two-particle quantum system in $\R^d$ with interaction and in presence of a random external potential field with a continuous argument (an Anderson model in a continuous space). Our aim is to establish the so-called Wegner-type…
We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two…
We analyze ground-state properties of strictly one-dimensional molecular matter comprised of identical particles of mass m. Such a class of systems can be described by an additive two-body potential whose functional form is common to all…
Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic…
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…
We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential $V$. Under suitable assumptions on $V$, using the monotonicity trick and the profile decomposition, we prove the existence of…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading…
We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy. For the ground state of quantum double or Levin-Wen model, we obtain a bound on the first order perturbation of…
A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…
Quantum phase transitions and observables of interest of the ground state in the Tavis-Cummings model are analyzed, for any number of atoms, by using a tensorial product of coherent states. It is found that this "trial" state constitutes a…
We show how the use of variational states to approximate the ground state of a system can be employed to study a multi-mode Dicke model. One of the main contributions of this work is the introduction of a not very commonly used quantity,…
In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p-Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the…
A system of two charged particles in a harmonic trap with additional magnetic field is considered. The problem is reduced to a single-particle one in relative coordinates. The ground- and lowest excited-state energies and wave functions are…
In this work, we present new connections between three types of quantum states: positive under partial transpose states, symmetric with positive coefficients states and invariant under realignment states. First, we obtain a common upper…
Wiener's criterion for the regularity of a boundary point with respect to the Dirichlet problem for the Laplace equation has been extended to various classes of elliptic and parabolic partial differential equations. They include linear…
Updating a probability distribution in the light of new evidence is a very basic operation in Bayesian probability theory. It is also known as state revision or simply as conditioning. This paper recalls how locally updating a joint state…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…