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Established methods for characterizing quantum information processes do not capture non-Markovian (history-dependent) behaviors that occur in real systems. These methods model a quantum process as a fixed map on the state space of a…
Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent many-body system, it can occur in an…
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 develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…
Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…
Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent…
We study the statistics and short-times dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite…
One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and…
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…
The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay…