24 citations · 80 across the 19 of their papers we have counts for
20 papers
On Normality Preserving Operations
Chokri Manai
We study arithmetic operations and maps which preserve normality. Revisiting a recent argument of Dayan, Ganguly and Weiss, we give a streamlined, self-contained presentation of th…
Correlation inequalities for transversal field models with application to quantum glasses
Chokri Manai, Simone Warzel
We study the class of transversal field models with pair interactions, including the quantum Curie-Weiss and the transversal field Ising model, as well as quantum spin glasses base…
Digit Mixing under Polynomial Maps
Chokri Manai
Let be a random number where we model the digits as independent Bernoulli random variables with possibly non-identical parameters $p_n=\mathbb{P}(…
The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model
Chokri Manai, Simone Warzel
We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington\--Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the qu…
Quantum Mean-Fields Spin Systems in a Random External Field
Chokri Manai
In this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despit…
Transcendence Meets Normality: Construction of Transcendentally Normal Numbers
Chokri Manai
In this work, we study real numbers for which is (absolutely) normal for every non-constant integer-valued polynomial . We call such numbers transcendentally normal.…
Dynamical Phase Diagram of the REM under independent spin-flips
Chokri Manai, Simone Warzel
We study the energy landscape of the Random Energy model (REM) integrated along trajectories of the simple random walk on the hypercube. We show that the quenched cumulant generati…
Super-Dense Sets and Their Role in the Theory of Normal Numbers
Chokri Manai
We introduce and study a new topological notion of the size for subsets of the real line, called \emph{super-density}. A set is super-dense if for every non-em…
The Quantum Random Energy Model is the Limit of Quantum -Spin Glasses
Anouar Kouraich, Chokri Manai, Simone Warzel
We consider the free energy of a class of spin glass models with -spin interactions in a transverse magnetic field. As , the infinite system-size free energy is…
A Parisi Formula for Quantum Spin Glasses
Chokri Manai, Simone Warzel
We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available…
Transcendental properties of entropy-constrained sets: Part II
Vjosa Blakaj, Chokri Manai
In this work, we address the question of the impossibility of certain single-letter formulas by exploiting the semi-algebraic nature of various entropy-constrained sets. The focus…
The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems
Chokri Manai, Simone Warzel
A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems w…
Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
Juan P. Garrahan, Chokri Manai, Simone Warzel
We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of non-interacting Ising spins. We mainly consider the case of all-to-all d…
Spectral Analysis of the Quantum Random Energy Model
Chokri Manai, Simone Warzel
The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type which describes effects of a transversal magnetic field on Derrida's spin glass. The model exhibits a gla…
The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
Chokri Manai, Simone Warzel
We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model…
Existence of replica-symmetry breaking in quantum glasses
Hajo Leschke, Chokri Manai, Rainer Ruder +1
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick…
Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams
Chokri Manai, Simone Warzel
We determine explicit variational expressions for the free energy of mean-field spin glasses in a transversal magnetic field, whose glass interaction is given by a hierarchical Gau…
The Quantum Random Energy Model as a Limit of p-Spin Interactions
Chokri Manai, Simone Warzel
We consider the free energy of a mean-field quantum spin glass described by a -spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \in…
Phase Diagram of the Quantum Random Energy Model
Chokri Manai, Simone Warzel
We prove Goldschmidt's formula [Phys. Rev. B 47 (1990) 4858] for the free energy of the quantum random energy model. In particular, we verify the location of the first order and th…
Totally odd depth-graded multiple zeta values and period polynomials
Charlotte Dietze, Chokri Manai, Christian Nöbel +1
Inspired by a paper of Tasaka, we study the relations between totally odd, motivic depth-graded multiple zeta values. Our main objective is to determine the rank of the matrix $C_{…