Finite-size localization scenarios in condensation transitions

Gabriele, Gotti,; Iubini, Stefano; Politi, Paolo

doi:10.1103/physreve.103.052133

Cited by 10 publications

(10 citation statements)

References 29 publications

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“…The equilibrium properties are well understood [22,25,27,28]. The system has a homogeneous phase for a 2 ⩽ h ⩽ 2a 2 and a condensed/localized phase for h > 2a 2 , characterized in the thermodynamic limit by a single site hosting a finite fraction of the whole energy, equal to (h − 2a 2 )N. Finite-size effects provide an interesting and unexpected scenario close to the critical line, h c = 2a 2 [24]. When h varies between the ground state h = a 2 and the upper value of the homogeneous phase, h = h c , the temperature varies between T = 0 and T = +∞.…”

Section: The Model and Its Equilibrium And Out-of-equilibrium Propertiesmentioning

confidence: 99%

“…h ≡ j h hold and stationary spatial profiles of mass and energy are defined respectively as a i = ⟨c i (t)⟩ and h i = ⟨c 2 i (t)⟩, where the symbol ⟨•⟩ 5 Three is the minimal number of sites allowing to satisfy conservation laws and letting the system evolve. When simulating the system at equilibrium the three sites may not be neighbours, which speeds up the relaxation to equilibrium [24], but in an out-of-equilibrium setup an update rule among distant sites would generate unphysical couplings between such sites.…”

Section: The Model and Its Equilibrium And Out-of-equilibrium Propertiesmentioning

confidence: 99%

“…The model was originally introduced to investigate the spontaneous onset of energy localization in the DNLS dynamics [17], but it has become a typical example of constraint-driven condensation [22][23][24]. In fact, depending on the densities of the two conserved quantities, a finite fraction of energy may eventually condense on a single site, a regime characterized by a negative absolute temperature [25,26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Onsager coefficients in a coupled-transport model displaying a condensation transition

Iubini

Politi

2023

New J. Phys.

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We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation of the Discrete Nonlinear Schr"odinger equation. This model is characterized by two conserved quantities, namely mass and energy; it displays a ``normal", homogeneous phase, separated by a condensed (negative-temperature) phase, where a macroscopic fraction of energy is localized on a single lattice site. When steadily maintained out of equilibrium by external reservoirs, the system exhibits coupled transport herein studied within the framework of linear response theory. We find that the Onsager coefficients satisfy an exact scaling relationship, which allows reducing their dependence on the thermodynamic variables to that on the energy density for unitary mass density. We also determine the structure of the nonequilibrium steady states in proximity of the critical line, proving the existence of paths which partially enter the condensed region. This phenomenon is a consequence of the Joule effect:the temperature increase induced by the mass current is so strong as to drive the system to negative temperatures. Finally, since the model attains a diverging temperature at finite energy, in such a limit the energy-mass conversion efficiency reaches the ideal Carnot value.

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Section: The Model and Its Equilibrium And Out-of-equilibrium Propertiesmentioning

confidence: 99%

Section: The Model and Its Equilibrium And Out-of-equilibrium Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Onsager coefficients in a coupled-transport model displaying a condensation transition

Iubini

Politi

2023

New J. Phys.

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“…As an instance, this behavior has been found and very precisely described in the framework of large deviation calculations and ensemble inequivalence in the case of mass-transport models [39,40] or for bosonic condensates in optical lattices described by the discrete non-linear Schrödinger equation (DNLSE) [41]. Concerning the DNLSE, it is known since almost two decades that his high energy phase is characterized by the appearance of localized breather-like solutions, which typically arise in certain regimes in models of non-linear waves [33,[42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Intensity pseudo-localized phase in the glassy random laser

Niedda¹,

Leuzzi²,

Gradenigo³

2023

J. Stat. Mech.

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Evidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor strictly condensed on few of them. Such a hybrid phase, recently characterized as a finite size effect in other models, such as the discrete non-linear Schrödinger equation, in the low temperature phase of the glassy random laser appears to be robust in the limit of large size.

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“…A "condensation" transition that separates between the typical-fluctuation regime, where the central limit theorem applies, and the distribution tail(s) where the big-jump principle applies, is a general phenomenon that has been observed in many instances [36,37]. Examples include the zero-range process [38], the discrete nonlinear Schrödinger equation [39][40][41][42][43], economic and financial models [44][45][46], mass-transport models [47][48][49][50][51][52][53][54][55], and run-and-tumble active particles [35,56,57]. Above a critical point in the tail of P (S; N ), a condensate appears meaning that one of the x i 's contirubes a macroscopic fraction to S. In the far tail this fraction approaches unity, so the big-jump principle is recovered.…”

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confidence: 99%

Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process

Smith

2021

Preprint

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We study the full distribution of A = T 0 x n (t) dt, n = 1, 2, . . . , where x (t) is an Ornstein-Uhlenbeck process. We find that for n > 2 the long-time (T → ∞) scaling form of the distribution is of the anomalous form P (A; T ) ∼ e −T µ fn(∆A/T ν ) where ∆A is the difference between A and its mean value, and the anomalous exponents are µ = 2/ (2n − 2), and ν = n/ (2n − 2). The rate function fn (y), that we calculate exactly, exhibits a first-order dynamical phase transition which separates between a homogeneous phase that describes the Gaussian distribution of typical fluctuations, and a "condensed" phase that describes the tails of the distribution. We also calculate the most likely realizations of A(t) = t 0 x n (s) ds and the distribution of x(t) at an intermediate time t conditioned on a given value of A. Extensions and implications to other continuous-time systems are discussed.

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Finite-size localization scenarios in condensation transitions

Cited by 10 publications

References 29 publications

Onsager coefficients in a coupled-transport model displaying a condensation transition

Onsager coefficients in a coupled-transport model displaying a condensation transition

Intensity pseudo-localized phase in the glassy random laser

Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process

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