相关论文: Asymptotics of the quantization errors for condens…
We present an analytical method to estimate the condensate fraction $n_0/n$ in strongly correlated systems for which the zero-temperature static structure factor $S({\bf p})$ is known. The advantage of the proposed method is that it allows…
Recent theoretical and experimental studies have given raise to new aspects in quantum measurements and error-disturbance uncertainty relations. After a brief review of these issues, we present an experimental test of the error-disturbance…
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
It is shown that Bose-Einstein condensation occurs for an ideal gas in two spatial dimensions in the presence of one impurity which is described quantum mechanically in terms of a point-like vortex and a contact interaction. This model is…
We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte Carlo simulation for various temperatures and compare the numerical result with simple approximative…
An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling…
We present a pedagogical introduction to Bose-Einstein condensation in traps with spherical symmetry, namely the spherical box and the thick shell, sometimes called bubble trap. In order to obtain the critical temperature for Bose-Einstein…
The multifractal spectrum of a Borel measure $\mu$ in $\mathbb{R}^n$ is defined as \[ f_\mu(\alpha) = \dim_H {x:\lim_{r\to 0} \frac{\log \mu(B(x,r))}{\log r}=\alpha}. \] For self-similar measures under the open set condition the behavior of…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
Let $\mu_1$ and $\mu_2$ be two complex-valued Borel measures on the real line such that $\operatorname{supp} \mu_1 =[\alpha_1,\beta_1] < \operatorname{supp} \mu_2 =[\alpha_2,\beta_2]$ and ${\rm d}\mu_i(x) = -\rho_i(x){\rm d}x/2\pi {\rm i}$,…
Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…
We prove effective equidistribution of expanding horocycles in $\mathrm{SL}_2(\mathbb{Z})\backslash\mathrm{SL}_2(\mathbb{R})$ with respect to various classes of Borel probability measures on $\mathbb{R}$ having certain Fourier asymptotics.…
In this paper we study the quantization problem for probability measures on Riemannian manifolds. Under a suitable assumption on the growth at infinity of the measure we find asymptotic estimates for the quantization error, generalizing the…
In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed…
We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…
For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification.…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the…
We have created a spatially homogeneous polariton condensate in thermal equilibrium, up to very high condensate fraction. Under these conditions, we have measured the coherence as a function of momentum, and determined the total coherent…