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Jean Richert

Publications and source records attributed to Jean Richert.

At least 19 recordsLinked to original sources
arXiv2023

A short note about the dynamical description of the measurement process in quantum physics

The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system interacting with the measuring device and show under which ideal conditions the measure process may ideally work. Our procedure leads to the conclusion that there is no hope that any experimental procedure will be able to lead to a clean solution of the process, except maybe in very specific cases. The reasons for this situation are deeply rooted in the fundamental properties of quantum theory.

quant-ph↗
arXiv2020

Open quantum systems at finite temperature

The consistent definition of the thermodynamic functions of small open quantum systems in contact with an environment in equilibrium with a heat bath has been the subject of many debates in the quantum community. In the present work we reproduce and comment parts of a recent approach of this subject by Rivas [15]. This approach overcomes the controversial discussions generated by the coupling between a system and its environment for any type of coupling between the two parts and allows for a consistent description of the thermodynamical properties of the system strongly interacting with the bath

quant-ph↗
arXiv2019

Entropy and applications of the area law in open quantum systems

Open quantum systems interact with their environment and their dynamical behaviour depends strongly both on the spectral properties of the environment and the structure of the interaction between the physical system and the environment. We examine the consequences of these spectral and structural properties on simple but general systems in the case of deterministic (non stochastic) interactions of arbitrary strength. The central point of interest concerns the role played by the semi-group property of the interaction in its relation with entropy and area laws properties of the system of interest.

quant-ph↗
arXiv2019

Evolution of open quantum systems: time scales, stochastic and continuous processes

The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a presentation of different aspects which characterize these systems and confront different physical situations which can be realized leading to systems which experience Markovian, non-Markovian, divisible or non-divisible interactions with the environments to which they are dynamically coupled. We aim to show how different approaches describe the evolution of quantum systems subject to different types of interactions with their environments.

quant-ph↗
arXiv2016

Quantum speed limit of a non-decoherent open system

We study the minimum time related to the quantum speed limit that characterizes the evolution of an open quantum system with the help of a simple model in the short and long time limits. We compare in particular the situation corresponding to a unique state and several states in the environment space. For short time intervals the results show a sensible difference in the behaviour of the system for different strengths of the interaction between the system and its environment.

quant-ph↗
arXiv2014

Different types of open quantum systems evolving in a Markovian regime

The interaction between an open quantum system and its environment induces generally memory effects generated by the fact that the response of the system to the environment is not instantaneous. Different physical reasons can be at the origin of an absence of time retardation. We present here a study of systems for which instantaneouness is realized although they do not necessarily follow established Markovian criteria.

quant-ph↗
arXiv2011

Propagation of local excitations through strongly correlated quantum chains

The propagation of an external transverse magnetic signal acting locally on a 1d chain of spins generates a disturbance which runs through the system. This quantum effect can be interpreted as a classical traveling wave which contains a superposition of a large set of frequencies depending on the size of the chain. Its local amplitude fixes the size of the z-component of the spins at any location in the chain. The average and maximum value of the group velocity are determined and compared with the transmission velocity fixed by the Lieb-Robinson upper bound inequality.

quant-ph↗
arXiv2010

Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method

The long-time dynamics of reaction-diffusion processes in low dimensions is dominated by fluctuation effects. The one-dimensional coagulation-diffusion process describes the kinetics of particles which freely hop between the sites of a chain and where upon encounter of two particles, one of them disappears with probability one. The empty-interval method has, since a long time, been a convenient tool for the exact calculation of time-dependent particle densities in this model. We generalise the empty-interval method by considering the probability distributions of two simultaneous empty intervals at a given distance. While the equations of motion of these probabilities reduce for the coagulation-diffusion process to a simple diffusion equation in the continuum limit, consistency with the single-interval distribution introduces several non-trivial boundary conditions which are solved for the first time for arbitrary initial configurations. In this way, exact space-time-dependent correlation functions can be directly obtained and their dynamic scaling behaviour is analysed for large classes of initial conditions.

cond-mat.stat-mech↗
arXiv2008

Interacting potential between spinons in the compact QED3 description of the Heisenberg model

We implement a Chern-Simons (CS) contribution into the compact QED3 description of the antiferromagnetic Heisenberg model in two dimensions at zero temperature. The CS term allows for the conservation of the SU(2) symmetry of the quantum spin system and fixes the flux through a plaquette to be a multiple of pi as was shown by Marston. We work out the string tension of the confining potential which acts between the spinons and show that the CS term induces a screening effect on the magnetic field only. The confining potential between spinons is not affected by the CS flux. The strict site-occupation by a single spin 1/2 is enforced by the introduction of an imaginary chemical potential constraint.

cond-mat.str-el↗
arXiv2007

Low energy properties of non-perturbative quantum systems: a space reduction approach

We propose and test a renormalization procedure which acts in Hilbert space. We test its efficiency on strongly correlated quantum spin systems by working out and analyzing the low-energy spectral properties of frustrated quantum spin systems in different parts of the phase diagram and in the neighbourhood of quantum critical points.

quant-ph↗
arXiv2006

An application of renormalization in Hilbert space at phase transition points in strongly interacting systems

We introduce an algorithm aimed to reduce the dimensions of Hilbert space. It is used here in order to study the behaviour of low energy states of strongly interacting quantum many-body systems at first order transitions and avoided crossings. The method is tested on different frustrated quantum spin ladders with two legs. The role and importance of symmetries are investigated by using different bases of states.

quant-ph↗
arXiv2006

Chiral symmetry restoration in (2+1)-dimensional $QED$ with a Maxwell-Chern-Simons term at finite temperature

We study the role played by a Chern-Simons contribution to the action in the $QED_3$ formulation of a two-dimensional Heisenberg model of quantum spin systems with a strictly fixed site occupation at finite temperature. We show how this contribution affects the screening of the potential which acts between spinons and contributes to the restoration of chiral symmetry in the spinon sector. The constant which characterizes the Chern-Simons term can be related to the critical temperature $T_c$ above which the dynamical mass goes to zero.

cond-mat.str-el↗