相关论文: Lifshits tails caused by anisotropic decay: the em…
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the…
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the…
A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to $\hbar$. While…
By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt…
We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem for the heat equation with random potential on $\Z^d$. We consider general i.i.d. potentials and show that exactly \emph{four} qualitatively different…
We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians $H^\omega=H_0+V^\omega$ on fractal spaces of infinite diameter. The kinetic term $H_0$ is given by…
Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion,…
The standard (``fine-grained'') interpretation of quantum density functional theory, in which densities are specified with infinitely-fine spatial resolution, is mathematically unruly. Here, a coarse-grained version of DFT, featuring…
We prove that, for a density of disorder $\rho$ small enough, a certain class of discrete random Schr\"odinger operators on $\Z^d$ with diluted potentials exhibits a Lifschitz behaviour from the bottom of the spectrum up to energies at a…
In quantum mechanical many-body systems, long-range and anisotropic interactions promote rich spatial structure and can lead to quantum frustration, giving rise to a wealth of complex, strongly correlated quantum phases. Long-range…
Geometrically frustrated interactions may render classical ground-states macroscopically degenerate. The connection between classical and quantum liquids and how the degeneracy is affected by quantum fluctuations is, however, less well…
An extensive investigation, both numerical and analytical, is performed for an anisotropic extension of the ferromagnetic spin-1 biquadratic model. The ground state phase diagram accommodates three symmetry-protected trivial phases, three…
We consider a two dimensional model of non-interacting chains of spinless fermions weakly coupled via a small inter-chain hopping and a repulsive inter-chain interaction. The phase diagram of this model has a surprising feature: an abrupt…
Quasiperiodic behaviour is known to occur in systems with enforced quasiperiodicity or randomness, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a setting where…
We study the behavior of the density of states and the $B_{1g}$ nematic susceptibility extracted from Raman response data across the doping-driven Lifshitz transition comparing the weak and strong interaction cases. Our results were…
We study the quantum phase transition in $f$-electron systems as a quantum Lifshitz transition driven by selective Mott localization in a realistic extended Anderson lattice model. Using DMFT, we find that a quantum critical {\it phase}…
It is known from density functional theory (DFT) calculations that RhSi has a multifold degenerate Dirac point at the Fermi energy, with the dominant states in the low-energy region displaying mostly Rh $d$ character. Using DFT+U, we…
The motivation for this article is to derive strict convexity of the surface tension for Lipschitz random surfaces, that is, for models of random Lipschitz functions from $\mathbb Z^d$ to $\mathbb Z$ or $\mathbb R$. An essential innovation…
This article concerns the tail probabilities of a light-tailed Markov-modulated L\'evy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of…
The Loschmidt echo is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential…