相关论文: Quantum and classical localisation, the spin quant…
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground…
Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…
We consider classical models of the kicked rotor type, with piecewise linear kicking potentials designed so that momentum changes only by multiples of a given constant. Their dynamics display quasi-localization of momentum, or quadratic…
The interplay between quantum Hall ordering and spontaneously broken "internal" symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel…
A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the…
We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The…
Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence.…
We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
We studied complex spectra of spin-two boson systems represented by E$\otimes$e and E$\otimes (b_1+b_2)$ Jahn-Teller models. For E$\otimes$e, at particular rotation quantum numbers we found a coexistence of up to three regions of the…
We introduce a conceptual reformulation of the Mott-Berezinski\u{i} (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping…
In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of…
We present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conduc- tivities semiclassically starting from the Kubo formula. The leading contribu- tion…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
In this work, we propose the quantum Hall system as a platform for exploring black hole phenomena. By exhibiting deep rooted commonalities between lowest Landau level and spacetime symmetries, we show that features of both quantum Hall and…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
Certain classical statistical systems with strong local constraints are known to exhibit Coulomb phases, where long-range correlation functions have power-law forms. Continuous transitions from these into ordered phases cannot be described…
We study the propagation of a hole in degenerate (paramagnetic) spin environments. This canonical problem has important connections to a number of physical systems, and is perfectly suited for experimental realization with ultra-cold atoms…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…