相关论文: Intermediate statistics in quantum maps
In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a…
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…
We derive single-particle and two-particle correlators of anyons in the presence of a magnetic field in the lowest Landau level. We show that the two-particle correlator exhibits signatures of fractional statistics which can distinguish…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
We discuss consequences of a recent observation that the sequence of periodic orbits in a chaotic billiard behaves like a poissonian stochastic process on small scales. This enables the semiclassical form factor $K_{sc}(\tau)$ to agree with…
We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the…
It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. Most results towards an affirmative answer have so far been restricted to almost sure…
Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…
The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation…
The difference of quantum mutual information for bipartite system of qubits and minimum taken with respect to local unitary transformation group is introduced as a characteristic of quantum correlations.The two qubits example (and…
Spectral statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold…