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Characterizing criticality in quantum many-body systems of dimension $\ge 2$ is one of the most important challenges of the contemporary physics. In principle, there is no generally valid theoretical method that could solve this problem. In…
Periodically-driven open quantum systems that never thermalize exhibit a discrete time-crystal behavior, a non-equilibrium quantum phenomenon that has shown promise in quantum information processing applications. Measurements of…
We study time dynamics of 1D disordered Heisenberg spin-1/2 chain focusing on a regime of large system sizes and a long time evolution. This regime is relevant for observation of many-body localization (MBL), a phenomenon that is expected…
This study investigates quantum-enhanced parameter estimation through continuous monitoring in open quantum systems that exhibit a dissipative time crystal phase. We first analytically derive the global quantum Fisher information (QFI) rate…
Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a…
Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of…
Novel dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be…
A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and…
I discuss the quantum dynamics of strongly disordered quantum systems with critically long range interactions, decaying as $1/r^{2d}$ in $d$ spatial dimensions. I argue that, contrary to expectations, localization in such systems is stable…
Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase…
The dark energy plus cold dark matter ($\Lambda$CDM) cosmological model has been a demonstrably successful framework for predicting and explaining the large-scale structure of Universe and its evolution with time. Yet on length scales…
I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find…
The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body…
We present new observational constraints on inhomogeneous models based on observables independent of the CMB and large-scale structure. Using Bayesian evidence we find very strong evidence for the homogeneous LCDM model, thus disfavouring…
We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the…
We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those…
Quantum many-body scars (QMBS) are exceptional eigenstates that defy thermalization, enabling long-lived coherent dynamics in strongly interacting systems. However, their stability under perturbations remains inadequately understood. In…
We establish a sharp criterion for the stability of a class of compactly supported, homogeneous density``minimal compact solitons'' or MCS states, of the time-dependent discrete nonlinear Schr\"odinger equation on a multi-lattice, $\mathbb…
Consider a discrete dynamical system given by a square matrix $M \in \mathbb{Q}^{d \times d}$ and a starting point $s \in \mathbb{Q}^d$. The orbit of such a system is the infinite trajectory $\langle s, Ms, M^2s, \ldots\rangle$. Given a…
We pinpoint the conditions necessary for discrete time crystal (DTC) formation in fully connected spin-cavity systems from the perspective of parametric resonance by mapping these systems onto oscillator like models. We elucidate the role…