Related papers: Mean field limit for bosons and infinite dimension…
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of $N$-particle systems. We establish an equation governing the evolution of our quantum analogue of the $N$-particle empirical…
Mesoscopic interacting Bose-Einstein condensates confined in a few traps display phase transitions that cannot be explained with a mean field theory. By describing each trap as an effective site of a Bose-Hubbard model and using the…
In this paper we extend the definitions of mean dimension and metric mean di-mension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean…
In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic)…
Explaining observed properties in terms of underlying shape degrees of freedom is a well--established prism with which to understand atomic nuclei. Self--consistent mean--field models provide one tool to understand nuclear shapes, and their…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the…
This paper concerns the derivation of the Kinetic Isothermal Euler system in dimension $d \geq 1$ from an N-particle system of extended charges with Coulomb interaction. This requires a combined mean field and quasineutral limit for a…
We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones.…
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
We study a quasi-two dimensional gas of bosonic dipoles, calculating the beyond mean field corrections to the ground state energy and chemical potential neglecting the transverse mode structure. We show that the corrections are sensitive to…
The competition between quantum many-particle dynamics and continuous monitoring can lead to measurement-induced phase transitions (MIPTs). So far, MIPTs have been extensively explored in fermionic or spin systems. To examine the…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
Bosons in a periodic lattice with on-site disorder at low but non-zero temperature are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the…