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We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous…
The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization…
Classical and quantum properties of a discontinuous perturbed twist map are investigated. Different classical diffusive regimes, quasilinear and slow respectively, are observed. The regime of slow classical diffusion gives rise to two…
For classical systems, expectation value of macroscopic property in equilibrium state can be typically provided through thermodynamic (so-called canonical) average, where summation is taken over possible states in phase space (or in…
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and…
We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
Understanding the emergence of classical behavior from a quantum theory is vital to establishing the quantum origin for the temperature fluctuations observed in the Cosmic Microwave Background (CMB). We show that a real-space approach can…
We consider the non-equilibrium behavior of a central spin system where the central spin is periodically reset to its ground state. The quantum mechanical evolution under this effectively dissipative dynamics is described by a discrete-time…
Quantum dot (QD) lay-outs are becoming more complex as the technology is being applied to more complex multi-QD structures. This increase in complexity requires improved capacitance modeling both for design and accurate interpretation of QD…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts…
Quantum systems in nonequilibrium conditions, where coherent many-body interactions compete with dissipative effects, can feature rich phase diagrams and emergent critical behavior. Associated collective effects, together with the…
We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength…
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its…
For any classical statistical-mechanics model with a discrete state space, and endowed with a dynamics satisfying detailed balance, it is possible to generalize the Rokhsar-Kivelson point for the quantum dimer model. That is, a quantum…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…