ترغب بنشر مسار تعليمي؟ اضغط هنا

Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices

52   0   0.0 ( 0 )
 نشر من قبل Claudio Castelnovo
 تاريخ النشر 2003
  مجال البحث فيزياء
والبحث باللغة English
 تأليف C. Castelnovo




اسأل ChatGPT حول البحث

Hard constraints imposed in statistical mechanics models can lead to interesting thermodynamical behaviors, but may at the same time raise obstructions in the thoroughfare to thermal equilibration. Here we study a variant of Baxters 3-color model in which local interactions and defects are included, and discuss its connection to triangular arrays of Josephson junctions of superconductors and textit{kagome} networks of superconducting wires. The model is equivalent to an Ising model in a hexagonal lattice with the constraint that the magnetization of each hexagon is $pm 6$ or 0. For ferromagnetic interactions, we find that the system is critical for a range of temperatures (critical line) that terminates when it undergoes an exotic first order phase transition with a jump from a zero magnetization state into the fully magnetized state at finite temperature. Dynamically, however, we find that the system becomes frozen into domains. The domain walls are made of perfectly straight segments, and domain growth appears frozen within the time scales studied with Monte Carlo simulations. This dynamical obstruction has its origin in the topology of the allowed reconfigurations in phase space, which consist of updates of closed loops of spins. As a consequence of the dynamical obstruction, there exists a dynamical temperature, lower than the (avoided) static critical temperature, at which the system is seen to jump from a ``supercooled liquid to a ``polycrystalline phase. In contrast, for antiferromagnetic interactions, we argue that the system orders for infinitesimal coupling because of the constraint, and we observe no interesting dynamical effects.



قيم البحث

اقرأ أيضاً

We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. These multiple critical temperatures correspond to crossing phases with different degrees of frustration.
We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system s charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.
Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the f orm of the so-called correlation hole, which is a dip below the saturation point of the survival probabilitys time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the timescales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size.
We classify the sectors of configurations that result from the dynamics of 2d crossing flux lines, which are the simplest degrees of freedom of the 3-coloring lattice model. We show that the dynamical obstruction is the consequence of two effects: (i ) conservation laws described by a set of invariants that are polynomials of the winding numbers of the loop configuration, (ii) steric obstruction that prevents paths between configurations, for lack of free space. We argue that the invariants fully classify the configurations in five, chiral and achiral, sectors and no further obstruction in the limit of low-winding numbers.
82 - Cecile Monthus 2021
The East model is the simplest one-dimensional kinetically-constrained model of $N$ spins with a trivial equilibrium that displays anomalously large spatio-temporal fluctuations, with characteristic space-time bubbles in trajectory space, and with a discontinuity at the origin for the first derivative of the scaled cumulant generating function of the total activity. These striking dynamical properties are revisited via the large deviations at Level 2.5 for the relevant local empirical densities and flows that only involve two consecutive spins. This framework allows to characterize their anomalous rate functions and to analyze the consequences for all the time-additive observables that can be reconstructed from them, both for the pure and for the random East model. These singularities in dynamical large deviations properties disappear when the hard-constraint of the East model is replaced by the soft constraint.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا