Exact dynamics in dual-unitary quantum circuits

We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs

On the Euler angles for SU(N)

In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the full range of the parameters, using both topological and geometrical methods. In particular, we show that the given parametrization realizes the group $SU(N+1)$ as a fibration of U(N) over the complex projective space $\mathbb{CP}^n$. This justifies the interpretation of the parameters as generalized Euler angles.Comment: 16 pages, references adde

Non equilibrium current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional \mc I (j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional \mc I . We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of \mc I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur

Charged Current Diffractive Structure Functions

We present our study of the diffraction in charged current DIS. We analyse the perturbatively tractable excitation of heavy quarks, emphasizing the peculiarities of the Regge factorization breaking in excitation of open charm.Comment: Proceeding of LISHEP98 workshop on diffractive physic

Long range correlations and phase transition in non-equilibrium diffusive systems

We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the occurrence of a phase transition as they become singular when the system approaches the transition

Off-diagonal helicity density matrix elements for heavy vector mesons inclusively produced in N-N, gamma-N, l-N interactions

Final state interactions in quark fragmentation may give origin to non zero values of the off-diagonal element rho_(1,-1) of the helicity density matrix of vector mesons V produced in current jets, with a large energy fraction x_E; the value of rho_(1,-1)(V) is related to the hard constituent dynamics and tests unusual properties of it. Some recent data on phi, K^* and D^* produced in e^+ e^- annihilations at LEP show such effects. Predictions are given here for rho_(1,-1) of heavy mesons produced in nucleon-nucleon, gamma-nucleon and lepton-nucleon interactions.Comment: LaTeX, 10 pages, 1 postscript figure, uses epsfig.sty. Revised version, to be published on Phys. Lett. B. Some statements added to clarify tex

Bioinorganic Chemistry

This book covers material that could be included in a one-quarter or one-semester course in bioinorganic chemistry for graduate students and advanced undergraduate students in chemistry or biochemistry. We believe that such a course should provide students with the background required to follow the research literature in the field. The topics were chosen to represent those areas of bioinorganic chemistry that are mature enough for textbook presentation. Although each chapter presents material at a more advanced level than that of bioinorganic textbooks published previously, the chapters are not specialized review articles. What we have attempted to do in each chapter is to teach the underlying principles of bioinorganic chemistry as well as outlining the state of knowledge in selected areas. We have chosen not to include abbreviated summaries of the inorganic chemistry, biochemistry, and spectroscopy that students may need as background in order to master the material presented. We instead assume that the instructor using this book will assign reading from relevant sources that is appropriate to the background of the students taking the course. For the convenience of the instructors, students, and other readers of this book, we have included an appendix that lists references to reviews of the research literature that we have found to be particularly useful in our courses on bioinorganic chemistry

A diffusive system driven by a battery or by a smoothly varying field

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit, the long range pair correlation functions of the system driven by a battery turn out to be very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models

Lagrangian phase transitions in nonequilibrium thermodynamic systems

In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in nonequilibrium this is not necessarily the case. We show that in nonequilibrium a new type of singularities can appear that are interpreted as phase transitions. In particular, this phenomenon occurs for the one-dimensional boundary driven weakly asymmetric exclusion process when the drift due to the external field is opposite to the one due to the external reservoirs, and strong enough.Comment: 10 pages, 2 figure

Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states

Nonequilibrium stationary states of thermodynamic systems dissipate a positive amount of energy per unit of time. If we consider transformations of such states that are realized by letting the driving depend on time, the amount of energy dissipated in an unbounded time window becomes then infinite. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work performed along any given transformation. We then show that the renormalized work satisfies a Clausius inequality and prove that equality is achieved for very slow transformations, that is in the quasi static limit. We finally connect the renormalized work to the quasi potential of the macroscopic fluctuation theory, that gives the probability of fluctuations in the stationary nonequilibrium ensemble