Related papers: Universality in quantum parametric correlations
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
Chaotic systems exhibit rich quantum dynamical behaviors ranging from dynamical localization to normal diffusion to ballistic motion. Dynamical localization and normal diffusion simulate electron motion in an impure crystal with a vanishing…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
We study distributions of eigenvalue curvatures for a block diagonal random matrix perturbed by a full random matrix. The most natural physical realization of this model is a quantum chaotic system with some inherent symmetry, such that its…
Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We…
The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study…
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle complex position, momentum and energy along a complex trajectory. On the basis of…
A transfer matrix formalism applicable to certain reparametrization invariant theories, including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt…
We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…
The present note contains the text of lectures discussing the problem of universality in fully developed turbulence. After a brief description of Kolmogorov's 1941 scaling theory of turbulence and a comparison between the statistical…
We expand on the investigation of the universal scaling properties in the early time behaviour of fast but smooth quantum quenches in a general $d$-dimensional conformal field theory deformed by a relevant operator of dimension $\Delta$…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
The functional defined as the squared modulus of the spatial average of the wave function squared, plays the role of an ``order parameter'' for the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
A generalization of the recently formulated nonlinear quantization of a parameterized theory is presented in the context of quantum gravity. The parametric quantization of a Friedmann universe with a massless scalar field is then considered…
We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the…