Related papers: Around quantum ergodicity
In this paper we study Spectral Decomposition Theorem [1] and translate it to quantum language by means of the Wigner transform. We obtain a quantum version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct…
A survey of the approach to Statistical Mechanics following Boltzmann's theory of ensembles and ergodic hypothesis leading to chaoticity as a unifying principle of equilibrium and nonequilibrium Statistical Mechanics.
We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix…
We show that in systems with highly degenerate energy spectra, such as the 2D transverse-field Ising model (2DTFIM) in the strong-field limit, quantum chaos can emerge in finite systems for arbitrary small perturbations. In this regime, the…
When a map is classically uniquely ergodic, it is expected that its quantization will posses quantum unique ergodicity. In this paper we give examples of Quantum Unique Ergodicity for the perturbed Kronecker map, and an upper bound for the…
We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z)$, which we take to be ergodic. Under some natural…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
Quantum gravitational corrections to the effective potential, at one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity ---which is taken as an effective theory for quantum…
An instability property of the Birkhoff's ergodic theorem and related asymptotic laws with respect to small violations of algorithmic randomness is studied. The Shannon--McMillan--Breiman theorem and all universal compression schemes are…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
Using the key properties of chaos, i.e. ergodicity and exponential instability, as a resource to control classical dynamics has a long and considerable history. However, in the context of controlling "chaotic" quantum unitary dynamics, the…
Apart from its debatable correctness, we examine the perturbative stability of the recently proposed cosmology from quantum potential. We find that the proposed quantum corrections invoke additional parameters which apparently introduce…
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
The concept of uncertainty quanta for a general system is introduced and applied to some important problems in physics and mathematics. EPR paradox gives new clue to the further understanding of particle correlation which turns out to be…
Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we…
We present in an informal way some recent results concerning a possible overlapping between classical unpredictability and quantum indeterminism.
Correlations between the parts of a many-body system, and its time dynamics, lie at the heart of sciences, and they can be classical as well as quantum. Quantum correlations are traditionally viewed as constituted out of classical…
The story on the early days of the Quantum Ergodic Theorem. Alternative proof, underlying heuristics, physical analogies and interpretations.
We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdi\`ere and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with…
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be…