Related papers: A note on the uniqueness result for the inverse He…
We investigate the entanglement in Hubbard models of hardcore bosons in $1D$, with an additional hardcore interaction on nearest neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of…
Envariance -- entanglement assisted invariance -- is a recently discovered symmetry of composite quantum systems. We show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Due to their exchange symmetry, identical particles can appear to be entangled -- another uniquely quantum…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made in such a way that the distribution of the particles matches a given…
We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to…
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this…
We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of…
The problem of a particle of mass m in the field of the inverse square potential is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate…
Weak-strong coupling duality relations are shown to be present in the quantum-mechanical many-body system with the interacting potential proportional to the pair-wise inverse-squared distance in addition to the harmonic potential. Using…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…
The classical and quantum dynamics of two particles constrained on $S^1$ is discussed via Dirac's approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also…
An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a…
We present a thermodynamic description of ultracold gases with dipolar interactions which properly accounts for the long-range nature and broken rotation invariance of the interactions. It involves an additional thermodynamic field…
Starting from the linearized BdG-equation we make the simple observation that pairing can occur between particles with total momenta different from zero, e.g., with equal momentum and opposite spin, in cases of an effective interaction…
The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing…
We call \emph{Alphabet model} a generalization to N types of particles of the classic ABC model. We have particles of different types stochastically evolving on a one dimensional lattice with an exchange dynamics. The rates of exchange are…