27 research outputs found
Polarized ensembles of random pure states
A new family of polarized ensembles of random pure states is presented. These
ensembles are obtained by linear superposition of two random pure states with
suitable distributions, and are quite manageable. We will use the obtained
results for two purposes: on the one hand we will be able to derive an
efficient strategy for sampling states from isopurity manifolds. On the other,
we will characterize the deviation of a pure quantum state from separability
under the influence of noise.Comment: 14 pages, 1 figur
A unified fluctuation formula for one-cut -ensembles of random matrices
Using a Coulomb gas approach, we compute the generating function of the
covariances of power traces for one-cut -ensembles of random matrices in
the limit of large matrix size. This formula depends only on the support of the
spectral density, and is therefore universal for a large class of models. This
allows us to derive a closed-form expression for the limiting covariances of an
arbitrary one-cut -ensemble. As particular cases of the main result we
consider the classical -Gaussian, -Wishart and -Jacobi
ensembles, for which we derive previously available results as well as new ones
within a unified simple framework. We also discuss the connections between the
problem of trace fluctuations for the Gaussian Unitary Ensemble and the
enumeration of planar maps.Comment: 16 pages, 4 figures, 3 tables. Revised version where references have
been added and typos correcte
Correlators for the Wigner–Smith time-delay matrix of chaotic cavities
We study the Wigner–Smith time-delay matrix Q of a ballistic quantum dot supporting N scattering channels. We compute the v-point correlators of the power traces Tr Qk for arbitrary v>1 at leading order for large N using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the Tr Qkʼs are integer-valued at leading order in N and include a MATHEMATICA code that computes their generating functions recursively
Condensation transition in joint large deviations of linear statistics
Real space condensation is known to occur in stochastic models of mass
transport in the regime in which the globally conserved mass density is greater
than a critical value. It has been shown within models with factorised
stationary states that the condensation can be understood in terms of sums of
independent and identically distributed random variables: these exhibit
condensation when they are conditioned to a large deviation of their sum. It is
well understood that the condensation, whereby one of the random variables
contributes a finite fraction to the sum, occurs only if the underlying
probability distribution (modulo exponential) is heavy-tailed, i.e. decaying
slower than exponential. Here we study a similar phenomenon in which
condensation is exhibited for non-heavy-tailed distributions, provided random
variables are additionally conditioned on a large deviation of certain linear
statistics. We provide a detailed theoretical analysis explaining the
phenomenon, which is supported by Monte Carlo simulations (for the case where
the additional constraint is the sample variance) and demonstrated in several
physical systems. Our results suggest that the condensation is a generic
phenomenon that pertains to both typical and rare events.Comment: 30 pages, 4 figures (minor revision
The semiclassical limit of a quantum Zeno dynamics
Motivated by a quantum Zeno dynamics in a cavity quantum electrodynamics setting, we study the asymptotics of a family of symbols corresponding to a truncated momentum operator, in the semiclassical limit of vanishing Planck constant h -> 0 and large quantum number N -> infinity, with hN kept fixed. In a suitable topology, the limit is the discontinuous symbol p chi(D) (x, p) where chi(D) is the characteristic function of the classically permitted region D in phase space. A refined analysis shows that the symbol is asymptotically close to the function p chi((N))(D) (x, p), where chi((N))(D) is a smooth version of chi(D) related to the integrated Airy function. We also discuss the limit from a dynamical point of view
Random matrices associated to Young diagrams
We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments are a generalization of the Catalan numbers. The limiting distribution is the density of a product of rescaled independent Beta random variables and its Stieltjes-Cauchy transform has a hypergeometric representation. In special cases we recover the Marchenko-Pastur and Dykema-Haagerup measures of square and triangular random matrices, respectively. We find a further factorization of the moments in terms of two complex-valued random variables that generalizes the factorization of the Marchenko-Pastur law as product of independent uniform and arcsine random variables
Generic aspects of the resource theory of quantum coherence
The class of incoherent operations induces a preorder on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two n-dimensional pure states are chosen independently according to the natural uniform distribution, then the probability that they are comparable vanishes as n→∞. We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-n asymptotic distribution. Our analysis is based on the observation that the extreme values (largest and smallest components) of a random point uniformly sampled from the unit simplex are distributed asymptotically as certain explicit homogeneous Markov chains