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The spectral gap - the energy difference between the ground state and first excited state - is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, existence of gapped topological spin liquid…
A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in…
Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…
We prove a volume-uniform effective-Hamiltonian theorem for bounded finite-range quantum spin systems on possibly infinite lattices. For any finite target region, we construct an energy-truncated Hamiltonian and prove a volume-uniform…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
Scrambling unitary dynamics in a quantum system transmutes local quantum information into a non-local web of correlations which manifests itself in a complex spatio-temporal pattern of entanglement. In such a context, we show there can…
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light-cone with exponentially decaying tails. We discuss several consequences of this…
We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density…
We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an…
Flaws in the process of modulation, or encoding of key bits in the quadratures of the electromagnetic light field, can make continuous-variable quantum key distribution systems susceptible to leakage of secret information. Here, we report…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these quantities can be strongly modified with respect to…
We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the…
Galilean invariance leaves its imprint on the energy spectrum and eigenstates of $N$ quantum particles, bosons or fermions, confined in a bounded domain. It endows the spectrum with a recurrent structure which in capillaries or elongated…
Dissipation is a ubiquitous phenomenon that affects the fate of chaotic quantum many-body dynamics. Here, we show that chaos can be robust against dissipation but can also assist and anomalously enhance relaxation. We compute exactly the…