arXiv subjects

Grégoire Ithier

Publications and source records attributed to Grégoire Ithier.

7 recordsLinked to original sources

arXiv2026

Identical Particle Systems : Hierarchical Spectral Reconstruction

We identify a hierarchical symmetry structure underlying the Hilbert space of quantum systems made of identical particles. By studying the linear map between single-body and many-body spectra, we show that the resulting spectral organization admits a natural partition into sectors induced by a symmetry governed by cyclotomic fields and their Galois groups. This approach offers a new perspective on the structure of quantum many-body spectra, defining a controlled coarse-graining of the Hilbert space in which degeneracies and spectral features can be systematically organized through a set of new quantum numbers. The resulting structure induces a hierarchy of spectral resolutions following a renormalization flow, which enables information loss control. We demonstrate that this hierarchical decomposition provides an efficient route to approximate MBDoS calculations for any identical particle system, while preserving physically relevant spectral properties. This approach provides a general symmetry-based framework for organizing and approximating many-body spectra, with potential applications to quantum thermalization, spectral statistics, and large-scale quantum simulations.

quant-ph↗

arXiv2024

Third sound detectors in accelerated motion

An accelerated observer moving through empty space sees particles appearing and disappearing, while an observer with a constant velocity does not register any particles. This phenomenon, generally known as the Unruh effect, relies on an initial vacuum state, thereby unifying the experience of all inertial observers. We propose an experiment to probe this observer-dependent detector response, using a laser beam in circular motion as a local detector of superfluid helium-4 surface modes or third sound waves. To assess experimental feasibility, we develop a theoretical framework to include a non-zero temperature initial state. We find that an acceleration-dependent signal persists, independent of the initial temperature. By introducing a signal-to-noise measure we show that observing this signal is within experimental reach.

gr-qc↗

arXiv2022

Many Body Density of States of a system of non interacting spinless fermions

The modeling of out-of-equilibrium many-body systems requires to go beyond the low-energy physics and local densities of states. Many-body localization, presence or lack of thermalization and quantum chaos are examples of phenomena in which states at different energy scales, including the highly excited ones, contribute to the dynamics and therefore affect the system's properties. Quantifying these contributions requires the many-body density of states (MBDoS), a function whose calculation becomes challenging even for non-interacting identical quantum particles due to the difficulty in enumerating states while enforcing the exchange symmetry. In the present work, we introduce a new approach to evaluate the MBDoS in the case of systems that can be mapped into free fermions. The starting point of our method is the principal component analysis of the filling matrix $F$ describing how $N$ fermions can be configured into $L$ single-particle energy levels. We show that the many body spectrum can be expanded as a weighted sum of spectra given by the principal components of the filling matrix. The weighting coefficients only involve renormalized energies obtained from the single body spectrum. We illustrate our method in two classes of problems that are mapped into spinless fermions: (i) non-interacting electrons in a homogeneous tight-binding model in 1D and 2D, and (ii) interacting spins in a chain under a transverse field.

cond-mat.stat-mech↗

arXiv2018

Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

We present a non perturbative calculation technique providing the mixed moments of the overlaps between the eigenvectors of two large quantum Hamiltonians: $\hat{H}_0$ and $\hat{H}_0+\hat{W}$, where $\hat{H}_0$ is deterministic and $\hat{W}$ is random. We apply this method to recover the second order moments or Local Density Of States in the case of an arbitrary fixed $\hat{H}_0$ and a Gaussian $\hat{W}$. Then we calculate the fourth order moments of the overlaps in the same setting. Such quantities are crucial for understanding the local dynamics of a large composite quantum system. In this case, $\hat{H}_0$ is the sum of the Hamiltonians of the system subparts and $\hat{W}$ is an interaction term. We test our predictions with numerical simulations.

quant-ph↗

arXiv2017

Typical equilibrium state of an embedded quantum system

We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded quantum system was established for several classes of random interactions. In other words, the time evolution of its quantum state does not depend on the microscopic details of the interaction. Focusing at the long time regime, we use this property to calculate analytically a new partition function characterizing the stationary state and involving the overlaps between eigenvectors of a bare and a dressed Hamiltonian. This partition function provides a new thermodynamical ensemble which includes the microcanonical and canonical ensembles as particular cases. We check our predictions with numerical simulations.

quant-ph↗

arXiv2017

Dynamical typicality of embedded quantum systems

We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in other words the fact that the reduced density matrix of the system has a self-averaging property. This phenomenon, which lies in a generalized central limit theorem, justifies rigorously averaging procedures over certain classes of random interactions and can explain the absence of sensitivity to microscopic details of irreversible processes such as thermalisation. It provides more generally a new ergodic principle for embedded quantum systems.

quant-ph↗

arXiv2015

Thermalisation of a quantum system from first principles

Why is thermalisation a universal phenomenon? How does a quantum system reach thermodynamical equilibrium? These questions are not new, dating even from the very birth of quantum theory and have been the subject of a renewed interest over the two last decades (see for instance the review in Eisert et al, Nature Physics 2015). In this work, we propose a universal model demonstrating that thermalisation of a small quantum system is an emergent property of the unitary evolution under a Schrödinger equation of a larger composite system, whose initial state can be arbitrary. We show that the origin of universality lies in the phenomenon of 'measure concentration', which provides self-averaging properties for the reduced density matrix characterizing the state of the small subsystem. Using our framework, we focus on the asymptotic state at long times and consider its stationary properties. In typical macroscopic conditions, we recover the canonical state and the Boltzmann distribution well known from statistical thermodynamics. This findings lead us to propose an alternative and more general definition of the canonical partition function which also allow us to describe non thermal stationary states.

quant-ph↗