اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBallistic transport in the classical Toda chain with harmonic pinning
82
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate, via numerical simulation, heat transport in the nonequilibrium stationary state (NESS) of the 1D classical Toda chain with an additional pinning potential, which destroys momentum conservation. The NESS is produced by coupling the system, via Langevin dynamics, to two reservoirs at different temperatures. To our surprise, we find that when the pinning is harmonic, the transport is ballistic. We also find that on a periodic ring with nonequilibrium initial conditions and no reservoirs, the energy current oscillates without decay. Lastly, Poincare sections of the 3-body case indicate that for all tested initial conditions, the dynamics occur on a 3-dimensional manifold. These observations suggest that the $N$-body Toda chain with harmonic pinning may be integrable. Alternatively, and more likely, this would be an example of a nonintegrable system without momentum conservation for which the heat flux is ballistic - contrary to all current expectations.
قيم البحث
اقرأ أيضاً
The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and eigenstates of the model are thus constructed simultaneously.
We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $beta^{-1}$. Given a fixed ${1leq m ll N}$, we prove that the
first $m$ integrals of motion of the periodic Toda chain are adiabatic invariants of FPUT (namely they are approximately constant along the Hamiltonian flow of the FPUT) for times of order $beta$, for initial data in a set of large measure. We also prove that special linear combinations of the harmonic energies are adiabatic invariants of the FPUT on the same time scale, whereas they become adiabatic invariants for all times for the Toda dynamics.
We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the models partition function by modding out the dynamical degrees of freedom of the su$(m|n)$ super
symmetric spin Sutherland model of $BC_N$ type, whose spectrum we fully determine. We then construct a generalized partition function depending polynomially on two sets of variables, which yields the standard one when evaluated at a suitable point. We show that this generalized partition function can be written in terms of two variants of the classical skew super Schur polynomials, which admit a combinatorial definition in terms of a new type of skew Young tableaux and border strips (or, equivalently, extended motifs). In this way we derive a remarkable description of the spectrum in terms of this new class of extended motifs, reminiscent of the analogous one for the closed Haldane-Shastry chain. We provide several concretes examples of this description, and in particular study in detail the su$(1|1)$ model finding an analytic expression for its Helmholtz free energy in the thermodynamic limit.
We examine the current driven dynamics for vortices interacting with conformal crystal pinning arrays and compare to the dynamics of vortices driven over random pinning arrays. We find that the pinning is enhanced in the conformal arrays over a wide
range of fields, consistent with previous results from flux gradient-driven simulations. At fields above this range, the effectiveness of the pinning in the moving vortex state can be enhanced in the random arrays compared to the conformal arrays, leading to crossing of the velocity-force curves.
We study the ballistic transport in integrable lattice models, i.e., the spin XXZ and Hubbard chains, close to the noninteracting limit. The stiffnesses of spin and charge currents reveal, at high temperatures, a discontinuous reduction (jump) when t
he interaction is introduced. We show that the jumps are related to the large degeneracy of the parent noninteracting models. These degeneracies are properly captured by the degenerate perturbation calculations which may be performed for large systems. We find that the discontinuities and the quasilocality of the conserved current in this limit can be traced back to the nonlocal character of an effective interaction. From the latter observation we identify a class of observables which show discontinuities in both models. We also argue that the known local conserved quantities are insufficient to explain the stiffnesses in the Hubbard chain in the regime of weak interaction.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
