اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamics of large deviations in the hydrodynamic limit: Non-interacting systems
294
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of non-interacting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semi-classical picture of quasi-particles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of non-interacting fermions and bosons are discussed.
قيم البحث
اقرأ أيضاً
We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially
resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.
We study the large deviations statistics of the intensive work done by changing globally a control parameter in a thermally isolated quantum many-body system. We show that, upon approaching a critical point, large deviations well below the mean work
display universal features related to the critical Casimir effect in the corresponding classical system. Large deviations well above the mean are, instead, of quantum nature and not captured by the quantum-to-classical correspondence. For a bosonic system we show that in this latter regime a transition from exponential to power-law statistics, analogous to the equilibrium Bose-Einstein condensation, may occur depending on the parameters of the quench and on the spatial dimensionality.
We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady stat
e is inherently connected to the presence of ballistically moving localised excitations. When such excitations are present, the system retains memory of initial correlations up to infinite times, thus evading decoherence. We demonstrate this connection in the context of the Luttinger model, the simplest quantum hydrodynamic model, and in the quantum KdV equation. In the standard Luttinger model, memory of all initial correlations is preserved throughout the time evolution up to infinitely large times, as a result of the purely ballistic dynamics. However nonlinear dispersion or interactions, when separately present, lead to spreading and delocalisation that suppress the above effect by eliminating the memory of non-Gaussian correlations. We show that, for any initial state that satisfies sufficient clustering of correlations, the steady state is Gaussian in terms of the bosonised or fermionised fields in the dispersive or interacting case respectively. On the other hand, when dispersion and interaction are simultaneously present, a semiclassical approximation suggests that localisation is restored as the two effects compensate each other and solitary waves are formed. Solitary waves, or simply solitons, are experimentally observed in quantum gases and theoretically predicted based on semiclassical approaches, but the question of their stability at the quantum level remains to a large extent an open problem. We give a general overview on the subject and discuss the relevance of our findings to general out of equilibrium problems.
We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functio
ns, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.
Using a Wigner function based approach, we study the Renyi entropy of a subsystem $A$ of a system of Bosons interacting with a local repulsive potential. The full system is assumed to be in thermal equilibrium at a temperature $T$ and density $rho$.
For a ${cal U}(N)$ symmetric model, we show that the Renyi entropy of the system in the large $N$ limit can be understood in terms of an effective non-interacting system with a spatially varying mean field potential, which has to be determined self consistently. The Renyi entropy is the sum of two terms: (a) Renyi entropy of this effective system and (b) the difference in thermal free energy between the effective system and the original translation invariant system, scaled by $T$. We determine the self consistent equation for this effective potential within a saddle point approximation. We use this formalism to look at one and two dimensional Bose gases on a lattice. In both cases, the potential profile is that of a square well, taking one value in the subsystem $A$ and a different value outside it. The potential varies in space near the boundary of the subsystem $A$ on the scale of density-density correlation length. The effect of interaction on the entanglement entropy density is determined by the ratio of the potential barrier to the temperature and peaks at an intermediate temperature, while the high and low temperature regimes are dominated by the non-interacting answer.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
