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Complex systems exhibit rich equilibrium states, yet the universal principles governing these systems remain unrevealed, motivating the search for novel experimental platforms. Random fiber lasers (RFLs), which generate partially-coherent…
Local excitations as carriers of quantum information spread out in the system in ways governed by the underlying interaction and symmetry. Understanding this phenomenon, also called quantum scrambling, is a prerequisite for employing…
Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, we investigate the interplay between the effects of disorder and periodic potentials in the integer…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
The out-of-time-order correlator (OTOC) of simple harmonic oscillator with extra anharmonic (quartic) interaction are calculated by the second quantization method. We obtain the analytic formulas of spectrum, Fock space states and matrix…
We show that the $N$-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the $N$-body ground state wave functions with two…
Response theory describes the reaction of observales to perturbations in external fields. We review this formalism for quantum fiels in isolation that have unitary time evolution. An emphasis is put on consequences of causality and the…
Discretizing the $\lambda \phi^4$ scalar field theory on a lattice yields a system of coupled anharmonic oscillators with quadratic and quartic potentials. We begin by analyzing the two coupled oscillators in the second quantization method…
Out-of-time ordered correlators are a probe of how the information of an initial perturbation is effectively scrambled under unitary time evolution, widely used to study quantum chaos. They have also been used to demonstrate that…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
Out-of-time-ordered correlation functions (OTOC's) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local…
We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterise many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered correlator. Due to the…
We develop a method to calculate generic time-dependent correlation functions for inhomogeneous quantum quenches in (1+1)-dimensional conformal field theory (CFT) induced by sudden Hamiltonian deformations that modulate the energy density…
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular nonabelian ones.…
Outcomes of measurements are characterized by an infinite family of generalized uncertainties, or cumulants, which provide information beyond the mean and variance of the observable. Here, we investigate the cumulants of a conserved charge…
For any weakly interacting particle system with bounded kernel, we give uniform-in-time estimates of the $L^2$ norm of correlation functions, provided that the diffusion coefficient is large enough. When the condition on the kernels is more…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…