اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe thermodynamic hamiltonian for open systems
431
0
0.0
(
0
)
تأليف
Umberto Lucia
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach have been introduced starting from non-equilibrium thermodynamics, obtaining the principle of maximum entropy generation for the open systems. This principle is a consequence of the lagrangian approach to the open systems. Here it will be developed a general approach to obtain the thermodynamic hamiltonian for the dynamical study of the open systems. It follows that the irreversibility seems to be the fundamental phenomenon which drives the evolution of the states of the open systems.
قيم البحث
اقرأ أيضاً
The dissipation generated during a quasistatic thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Here, we show how
to generalize this approach to open quantum systems by finding the thermodynamic metric associated to a given Lindblad master equation. The obtained metric can be understood as a perturbation over the background geometry of equilibrium Gibbs states, which is induced by the Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on two paradigmatic examples: an Ising chain and a two-level system interacting with a bosonic bath with different spectral densities.
The principle of maximum irreversible is proved to be a consequence of a stochastic order of the paths inside the phase space; indeed, the system evolves on the greatest path in the stochastic order. The result obtained is that, at the stability, the
entropy generation is maximum and, this maximum value is consequence of the stochastic order of the paths in the phase space, while, conversely, the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation at the stability.
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g. in quantum annealing and in studies of topological properties of matter. In this setup, the rate of
variation $varepsilon$ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this letter, we prove a version of the adiabatic theorem for gapped ground states of quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo linear response formula for a broad class of gapped interacting systems.
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 investigate the problem of determining the Hamiltonian of a locally interacting open-quantum system. To do so, we construct model estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion which rely o
n a polynomial number of measurements and parameters. We validate our Hamiltonian assignment methods by numerically simulating one-dimensional XX-interacting spin chains coupled to thermal reservoirs. We study Hamiltonian learning in the presence of systematic noise and find that, in certain time dependent cases, the Hamiltonian estimator accuracy increases when relaxing the environments physicality constraints.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
