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We show that in small and low density systems described by a lattice gas model with fixed number of particles the location of a thermodynamic phase transition can be detected by means of the distribution of the fluctuations related to an…
An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as…
We establish rigourously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n to infinity and the thermodynamic limit N to infinity taken. In this limit the…
We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for…
A key feature of non-equilibrium thermodynamics is the Markovian, deterministic relaxation of coarse observables such as, for example, the temperature difference between two macroscopic objects which evolves independently of almost all…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…
We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.
The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…
Phase transitions are emergent phenomena where microscopic interactions drive a disordered system into a collectively ordered phase. Near the boundary between two phases, the system can exhibit critical, scale-invariant behavior. Here, we…
We investigate the Fano-Anderson model coupled to a large ensemble of spins under the influence of an external magnetic field. The interaction between the two spin systems is treated within a meanfield-approach and we assume an anisotropic…
The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most…
Several methods are proposed for the analysis, visualization and interpretation of high-dimensional spin system trajectories produced by quantum mechanical simulations. It is noted that expectation values of specific observables in large…
Considering the standard abelian sandpile model in one dimension, we construct an infinite volume Markov process corresponding to its thermodynamic (infinite volume) limit. The main difficulty we overcome is the strong non-locality of the…
We study scrambling in connection to multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are…
We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained,…
By analysing an n-dimensional generalisation of Thomas's cyclically symmetric attractor we find that this chaotic dynamical system behaves like a random walk constrained onto the surface of a hypersphere. The growth of error is limited,…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
We show the existence of fragile-to-strong transitions in kinetically constrained systems by studying the equilibrium and out-of-equilibrium dynamics of a generic constrained Ising spin chain which interpolates between the symmetric and…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…