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Publications 2022

    Publications de l'année 2022 :

  • Algebraic area enumeration of random walks on the honeycomb lattice – Archive ouverte HAL

    Li Gan 1 Stéphane Ouvry 1 Alexios P. Polychronakos

    Li Gan, Stéphane Ouvry, Alexios P. Polychronakos. Algebraic area enumeration of random walks on the honeycomb lattice. Phys.Rev.E, 2022, 105 (1), pp.014112. ⟨10.1103/PhysRevE.105.014112⟩. ⟨hal-03318233⟩

    We study the enumeration of closed walks of given length and algebraic area on the honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we map the problem to a Hofstadter-like Hamiltonian and show that the generating function of closed walks maps to the grand partition function of a system of particles with exclusion statistics of order

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Barrier billiard and random matrices – Archive ouverte HAL

    Eugene Bogomolny 1

    Eugene Bogomolny. Barrier billiard and random matrices. J.Phys.A, 2022, 55, pp.024001. ⟨10.1088/1751-8121/ac3da6⟩. ⟨hal-03531732⟩

    The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with a barrier in the centre can be reduced to the investigation of a certain unitary matrix. Under heuristic assumptions this matrix is substituted by a special low-complexity random unitary matrix of independent interest. The main results of the paper are (i) spectral statistics of such billiards is insensitive to the barrier height and (ii) it is well described by the semi-Poisson distributions.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Edge fluctuations and third-order phase transition in harmonically confined long-range systems – Archive ouverte HAL

    Jitendra KethepalliManas KulkarniAnupam KunduSatya N. Majumdar 1 David MukamelGregory Schehr 2

    Jitendra Kethepalli, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, David Mukamel, et al.. Edge fluctuations and third-order phase transition in harmonically confined long-range systems. J.Stat.Mech., 2022, 2203 (3), pp.033203. ⟨10.1088/1742-5468/ac52b2⟩. ⟨hal-03481889⟩

    We study the distribution of the position of the rightmost particle x $_{max}$ in a N-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive potential, of the form r $^{−k}$ with −2 < k < ∞ where r is the inter-particle distance. In equilibrium at temperature O(1), the gas settles on a finite length scale L $_{N}$ that depends on N and k. We numerically observe that the typical fluctuation of y $_{max}$ = x $_{max}$/L $_{N}$ around its mean is of . Over this length scale, the distribution of the typical fluctuations has a N independent scaling form. We show that the exponent η $_{k}$ obtained from the Hessian theory predicts the scale of typical fluctuations remarkably well. The distribution of atypical fluctuations to the left and right of the mean ⟨y $_{max}$⟩ are governed by the left and right large deviation functions (LDFs), respectively. We compute these LDFs explicitly ∀ k > −2. We also find that these LDFs describe a pulled to pushed type phase transition as observed in Dyson’s log-gas (k → 0) and 1d one component plasma (k = −1). Remarkably, we find that the phase transition remains third order for the entire regime. Our results demonstrate the striking universality of the third order transition even in models that fall outside the paradigm of Coulomb systems and the random matrix theory. We numerically verify our analytical expressions of the LDFs via Monte Carlo simulation using an importance sampling algorithm.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
    • 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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  • Eightfold way to dark states in SU(3) cold gases with two-body losses – Archive ouverte HAL

    Lorenzo Rosso 1 Leonardo Mazza 1 Alberto Biella 1

    Lorenzo Rosso, Leonardo Mazza, Alberto Biella. Eightfold way to dark states in SU(3) cold gases with two-body losses. Phys.Rev.A, 2022, 105, pp.L051302. ⟨10.1103/PhysRevA.105.L051302⟩. ⟨hal-03572985⟩

    We study the quantum dynamics of a one-dimensional SU(3)-symmetric system of cold atoms in the presence of two-body losses. We exploit the representation theory of SU(3), the so-called eightfold way, as a scheme to organize the dark states of the dissipative dynamics in terms of generalized Dicke states and show how they are dynamically approached, both in the weakly- and and strongly-interacting and dissipative regimes. Our results are relevant for a wide class of alkaline-earth(-like) gases experiments, paving the way to the dissipative preparation and exploitation of generalized Dicke states.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Global Quenches after Localized Perturbations – Archive ouverte HAL

    Maurizio Fagotti 1

    Maurizio Fagotti. Global Quenches after Localized Perturbations. Phys.Rev.Lett., 2022, 128 (11), pp.110602. ⟨10.1103/PhysRevLett.128.110602⟩. ⟨hal-03413343⟩

    We investigate the effect of a single spin flip preceding a global quench between translationally invariant local Hamiltonians in spin-

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Kinetic formation of trimers and multimers in a spinless fermionic chain – Archive ouverte HAL

    Lorenzo Gotta 1 Leonardo Mazza 1 Pascal Simon 2 Guillaume Roux 1

    Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux. Kinetic formation of trimers and multimers in a spinless fermionic chain. Phys.Rev.B, 2022, 105 (13), pp.134512. ⟨10.1103/PhysRevB.105.134512⟩. ⟨hal-03467325⟩

    We study a chain of spinless fermions with a multimer hopping term which kinematically favors the formation of multimers and competes with single-particle hopping. We argue that this model generically stabilizes two different multimer phases, as well as intermediate phases where the free-fermion and multimer fluids coexist and do not spatially separate. Using density-matrix renormalization group techniques, we establish the phase diagram of the model in the case of trimers. For one of the intermediate phases, hybridization between the fermions and trimers liquids does occur and the onset of their correlations is well captured by a generalized BCS-like ansatz. The case of tetramers is finally addressed.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
    • 2. LPS - Laboratoire de Physique des Solides

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  • Level compressibility of certain random unitary matrices – Archive ouverte HAL

    Eugene Bogomolny 1

    Eugene Bogomolny. Level compressibility of certain random unitary matrices. Entropy, 2022, 24 (6), pp.795. ⟨10.3390/e24060795⟩. ⟨hal-03601297⟩

    The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing models with intermediate spectral statistics. The computations are based on the approach developed by G. Tanner in [J. Phys. A: Math. Gen. 34, 8485 (2001)] for chaotic systems. The main ingredient of the method is the determination of eigenvalues of a transition matrix whose matrix elements equal squared moduli of matrix elements of the initial unitary matrix. The principal result of the paper is the proof that the level compressibility of random unitary matrices derived from the exact quantisation of barrier billiards and consequently of barrier billiards themselves is equal to $1/2$ irrespectively of the height and the position of the barrier.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Measurable fractional spin for quantum Hall quasiparticles on the disk – Archive ouverte HAL

    Tommaso Comparin 1 Alvin Opler 2 Elia MacalusoAlberto Biella 2 Alexios P. PolychronakosLeonardo Mazza 2

    Tommaso Comparin, Alvin Opler, Elia Macaluso, Alberto Biella, Alexios P. Polychronakos, et al.. Measurable fractional spin for quantum Hall quasiparticles on the disk. Phys.Rev.B, 2022, 105 (8), pp.085125. ⟨10.1103/PhysRevB.105.085125⟩. ⟨hal-03496472⟩

    We study the spin of the localized quasiparticle excitations of lowest-Landau-level quantum Hall states defined on a disk. The spin that we propose satisfies the spin-statistics relation and can be used to reconstruct the topological geometric phase associated to the exchange of two arbitrarily chosen quasiparticles. Since it is related to the quadrupole moment of the quasiparticle charge distribution, it can be measured in an experiment and could reveal anyonic properties in a way that is complementary to the interferometric schemes employed so far. We first discuss our definition for the quasiholes of the Laughlin state, for which we present a numerical and analytical study of our spin, and we proceed with a discussion of several kinds of quasiholes of the Halperin 221 state. Finally, we discuss the link between our spin and the adiabatic rotation of the quasiparticles around their axis and demonstrate that our spin obeys the spin-statistics relation.

    • 1. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
    • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Random matrices associated with general barrier billiards – Archive ouverte HAL

    Eugene Bogomolny 1

    Eugene Bogomolny. Random matrices associated with general barrier billiards. J.Phys.A, 2022, 55 (25), pp.254002. ⟨10.1088/1751-8121/ac6f31⟩. ⟨hal-03433054⟩

    The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted from the exact billiard quantisation condition by applying a random phase approximation for high-excited states. An important ingredient of the method is the calculation of S-matrix for the scattering in the slab with a half-plane inside by the Wiener–Hopf method. It appears that these random matrices have the form similar to the one obtained by the author in (2022 J. Phys. A: Math. Theor. 55 024001) for a particular case of symmetric barrier billiards but with different choices of parameters. The local correlation functions of the resulting random matrices are well approximated by the semi-Poisson distribution which is a characteristic feature of various models with intermediate statistics. Consequently, local spectral statistics of the considered barrier billiards is (i) universal for almost all values of parameters and (ii) well described by the semi-Poisson statistics.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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  • Record statistics for random walks and L\’evy flights with resetting – Archive ouverte HAL

    Satya N. Majumdar 1 Philippe Mounaix 2 Sanjib Sabhapandit 3 Gregory Schehr 4

    Satya N. Majumdar, Philippe Mounaix, Sanjib Sabhapandit, Gregory Schehr. Record statistics for random walks and L\'evy flights with resetting. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2022. ⟨hal-03534126⟩

    We compute exactly the mean number of records $\langle R_N \rangle$ for a time-series of size $N$ whose entries represent the positions of a discrete time random walker on the line. At each time step, the walker jumps by a length $\eta$ drawn independently from a symmetric and continuous distribution $f(\eta)$ with probability $1-r$ (with $0\leq r < 1$) and with the complementary probability $r$ it resets to its starting point $x=0$. This is an exactly solvable example of a weakly correlated time-series that interpolates between a strongly correlated random walk series (for $r=0$) and an uncorrelated time-series (for $(1-r) \ll 1$). Remarkably, we found that for every fixed $r \in [0,1[$ and any $N$, the mean number of records $\langle R_N \rangle$ is completely universal, i.e., independent of the jump distribution $f(\eta)$. In particular, for large $N$, we show that $\langle R_N \rangle$ grows very slowly with increasing $N$ as $\langle R_N \rangle \approx (1/\sqrt{r})\, \ln N$ for $0

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
    • 2. CPHT - Centre de Physique Théorique [Palaiseau]
    • 3. Raman Research Institute
    • 4. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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  • Topological superfluid transition in bubble-trapped condensates – Archive ouverte HAL

    Andrea Tononi 1 Axel PelsterLuca Salasnich

    Andrea Tononi, Axel Pelster, Luca Salasnich. Topological superfluid transition in bubble-trapped condensates. Physical Review Research, American Physical Society, 2022, 4 (1), pp.013122. ⟨10.1103/PhysRevResearch.4.013122⟩. ⟨hal-03587470⟩

    Ultracold quantum gases are highly controllable and, thus, capable of simulating difficult quantum many-body problems ranging from condensed matter physics to astrophysics. Although experimental realizations have so far been restricted to flat geometries, recently also curved quantum systems, with the prospect of exploring tunable geometries, are produced in microgravity facilities as ground-based experiments are technically limited. Here we analyze bubble-trapped condensates, in which the atoms are confined on the surface of a thin spherically-symmetric shell by means of external magnetic fields. A thermally-induced proliferation of vorticity yields a vanishing of superfluidity. We describe the occurrence of this topological transition by conceptually extending the theory of Berezinskii, Kosterlitz and Thouless for infinite uniform systems to such finite-size systems. Unexpectedly, we find universal scaling relations for the mean critical temperature and the finite width of the superfluid transition. Furthermore, we elucidate how they could be experimentally observed in finite-temperature hydrodynamic excitations.

    • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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