Related papers: Typicality in random matrix product states
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
The trade-off between the two types of errors in binary state discrimination may be quantified in the asymptotics by various error exponents. In the case of simple i.i.d. hypotheses, each of these exponents is equal to a divergence…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…
We reformulate slightly Russell's notion of typicality, so as to eliminate its circularity and make it applicable to elements of any first-order structure. We argue that the notion parallels Martin-L\"{o}f (ML) randomness, in the sense that…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products…
Bennett et al. \cite{BDF+99} identified a set of orthogonal {\em product} states in the $3\otimes 3$ Hilbert space such that reliably distinguishing those states requires non-local quantum operations. While more examples have been found for…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
We show insurmountable contradictions which arise if statistical ensembles are considered a consequence of the influence of the environment of the physical systems. We regard the multiplicity of states with a definite energy value as a…
The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Statistical mechanics for states with complex eigenvalues, which are described by Gel'fand triplet and represent unstable states like resonances, are discussed on the basis of principle of equal ${\it a priori}$ probability. A new entropy…
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.