Found 1475 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Black Hole Interiors via Spin Models

We test the conjecture that a particular

**mean****field**Hamiltonian provides such a local bulk Hamiltonian by numerically solving the exact Schrodinger equation and comparing the time evolution to the approximate mean field time values. Expand abstract. To model the interior of a black hole, a study is made of a spin system with long-range random four-spin couplings that exhibits quantum chaos. The black hole limit corresponds to a system where the microstates are approximately degenerate and equally likely, corresponding to the high temperature limit of the spin system. At the leading level of approximation, reconstruction of bulk physics implies that local probes of the black hole should exhibit free propagation and unitary local evolution. We test the conjecture that a particular

**mean****field**Hamiltonian provides such a local bulk Hamiltonian by numerically solving the exact Schrodinger equation and comparing the time evolution to the approximate**mean****field**time values. We find excellent agreement between the two time evolutions for timescales smaller than the scrambling time. In earlier work, it was shown bulk evolution along comparable timeslices is spoiled by the presence of the curvature singularity, thus the matching found in the present work provides evidence of the success of this approach to interior holography. The numerical solutions also provide a useful testing ground for various measures of quantum chaos and global scrambling. A number of different observables, such as entanglement entropy, out-of-time-order correlators, and trace distance are used to study these effects. This leads to a suitable definition of scrambling time, and evidence is presented showing a logarithmic variation with the system size.103 days ago

4/10 relevant

arXiv

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arXiv

Local-**field** Theory of the BCS-BEC Crossover

We develop a self-consistent theory unifying the description of a quantum Fermi gas in the presence of a Fano-Feshbach resonance in the whole phase diagram ranging from BCS to BEC type of superfluidity and from narrow to broad resonances, including the fluctuations beyond

**mean****field**. Expand abstract. We develop a self-consistent theory unifying the description of a quantum Fermi gas in the presence of a Fano-Feshbach resonance in the whole phase diagram ranging from BCS to BEC type of superfluidity and from narrow to broad resonances, including the fluctuations beyond

**mean****field**. Our theory covers a part of the phase diagram which is not easily accessible by Quantum Monte Carlo simulations and is becoming interesting for a new class of experiments in cold atoms.104 days ago

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arXiv

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arXiv

Cell Model Approaches for Predicting the Swelling and Mechanical Properties of Polyelectrolyte Gels

The second

**mean**-**field**step integrates out the degrees of freedom of the flexible chain and the ions. Expand abstract. We present two successive

**mean**-**field**approximations for describing the mechanical properties and the swelling equilibrium of polyelectrolyte gels in contact with a salt solution. The first**mean**-**field**approximation reduces the many-chain problem of a gel to a corresponding single chain problem. The second**mean**-**field**step integrates out the degrees of freedom of the flexible chain and the ions. It replaces the particle-based description of the polyelectrolyte with suitable charge distributions and an effective elasticity term. These simplifications result in a computationally very efficient Poisson-Boltzmann cell-gel description. Despite their simplicity, the single chain cell-gel model shows excellent and the PB model very good agreement with explicit molecular dynamics simulations of the reference periodic monodisperse network model for varying chain length, polymer charge fraction, and external reservoir salt concentrations. Comparisons of our models to the Katchalsky model reveal that our approach is superior for strongly charged chains and can also predict the bulk moduli more accurately. We further discuss chain length polydispersity effects, investigate changes in the solvent permittivity, and demonstrate the robustness of our approach to parameter variations coming from several modeling assumptions.104 days ago

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arXiv

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arXiv

Model for heterogeneous reaction-diffusion systems with application to one epidemic

Both the detailed and the

**mean**-**field**models are solved by**means**of the standard finite volume method. Expand abstract. The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One synthetic epidemic system with short range heterogeneous composition is modelled and its space-time evolution studied using maximum heterogeneity details. Two other modelling alternatives are applied, one of them using elementary

**mean**-**field**variables, one other using non-localized geometrical parameters, so avoiding the limitations of the used**mean**-**field**model, while keeping significant features of more detailed models. Both the detailed and the**mean**-**field**models are solved by**means**of the standard finite volume method. The model with less defined geometry is solved by**means**of one modified version of the finite volume method. Simulation results of the three models are compared. At the high diffusion range all models behave similarly. At moderate diffusion fluxes, the numerical results of the model with reduced geometric details are in excellent agreement with the results of the detailed model. The simple**mean**-**field**model presents limited accuracy at low and moderate values of the diffusion coefficient.108 days ago

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arXiv

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arXiv

Elastic avalanches reveal marginal behaviour in amorphous solids

In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the

**mean****field**predictions for systems above the jamming transition. Expand abstract. Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical

**mean****field**calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the**mean****field**predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.109 days ago

4/10 relevant

arXiv

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arXiv

Discrete-time average-cost **mean**-**field** games on Polish spaces

Then, we show that the equilibrium policy in the

**mean**-**field**game, when adopted by each agent, is an approximate Nash equilibrium for the corresponding finite-agent game with sufficiently many agents. Expand abstract. In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of the problem. In the infinite population limit, a generic agent is faced with a \emph{so-called}

**mean**-**field**game. In this paper, we study discrete-time**mean**-**field**games with average-cost criteria. Using average cost optimality equation and Kakutani's fixed point theorem, we establish the existence of Nash equilibria for**mean**-**field**games under drift and minorization conditions on the dynamics of each agent. Then, we show that the equilibrium policy in the**mean**-**field**game, when adopted by each agent, is an approximate Nash equilibrium for the corresponding finite-agent game with sufficiently many agents.110 days ago

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arXiv

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arXiv

Fermionic entanglement in the Lipkin model

We finally show that the first measures and the up-down reduced entanglement can be correctly described through a basic

**mean**-**field**approach supplemented with symmetry restoration, whereas the concurrence requires at least the inclusion of RPA-type correlations for a proper prediction. Expand abstract. We examine the fermionic entanglement in the ground state of the fermionic Lipkin model and its relation with bipartite entanglement. It is first shown that the one-body entanglement entropy, which quantifies the minimum distance to a fermionic Gaussian state, behaves similarly to the

**mean**-**field**order parameter and is essentially proportional to the total bipartite entanglement between the upper and lower modes, a quantity meaningful only in the fermionic realization of the model. We also analyze the entanglement of the reduced state of four single-particle modes (two up-down pairs), showing that its fermionic concurrence is strongly peaked at the phase transition and behaves differently from the corresponding up-down entanglement. We finally show that the first measures and the up-down reduced entanglement can be correctly described through a basic**mean**-**field**approach supplemented with symmetry restoration, whereas the concurrence requires at least the inclusion of RPA-type correlations for a proper prediction. Fermionic separability is also discussed.110 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Dynamical slave-boson **mean**-**field** study of the Mott transition in the
Hubbard model in the large-$z$ limit

The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $z$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. Expand abstract.

The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson

**mean**-**field**theory in the limit of large lattice coordination number $z$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $1/\sqrt{z}$, and becomes exact on the infinite-$z$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard $U_c$ and the corresponding doublon density $n_d^c$, hopping $\chi_d^c$ and doublon-holon pairing $\Delta_d^c$ amplitudes. We find $U_c=U_{\rm BR} [1 -2n_d^c -\sqrt{z} (\chi_d^c +\Delta_d^c))] \simeq0.8U_{\rm BR}$, where $U_{\rm BR}$ is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static**mean**-**field**solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical**mean**-**field**theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a $U(1)$ quantum spin liquid with nonzero intersite spinon hopping that survives the large-$z$ limit and lifts the $2^N$-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact $U(1)$ gauge**field**in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.110 days ago

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arXiv

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arXiv

The selection problem for some first-order stationary **mean**-**field** games

Using ideas from Aubry-Mather theory, we establish a selection criterion for the limit. Expand abstract.

Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence of the vanishing-discount limit to a unique solution up to constants. Then, we establish refined asymptotics for the limit. When those conditions do not hold, the limit problem may not have a unique solution and its solutions may not be smooth, as we illustrate in an elementary example. Finally, we investigate the stability of regular weak solutions and address the selection problem. Using ideas from Aubry-Mather theory, we establish a selection criterion for the limit.

114 days ago

8/10 relevant

arXiv

8/10 relevant

arXiv

Magnetic Entropy in a Non-Collinear Weak Ferromagnetic YCrO3

The maximum entropy change fits well with

**mean****field**approximation at higher**fields**, while the observed deviation in lower field substantiates the onset of weak ferromagnetism in YCrO3. Expand abstract. We carried out temperature and

**field**dependent magnetic measurements to understand the evolution of magnetic non-collinearity near antiferromagnetic phase in conjunction with the evolution of magnetic entropy near phase transition. We observed the maximum change in entropy just before magnetic ordering of Cr3+ in YCrO3 with the maximum change in magnetic entropy of -0.38 Jkg-1K-1 at 8 Tesla external**field**. The data is linear in higher**fields**3 T - 8 T , whereas it showed deviations in the lower**field**region. The maximum entropy change fits well with**mean****field**approximation at higher fields, while the observed deviation in lower**field**substantiates the onset of weak ferromagnetism in YCrO3.114 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv