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Register a new userThermalization and possible quantum relaxation times in classical fluids: theory and experiment
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Quantum effects in material systems are often pronounced at low energies and become insignificant at high temperatures. We find that, perhaps counterintuitively, certain quantum effects may follow the opposite route and become sharp when extrapolated to high temperature within a classical liquid phase. In the current work, we suggest basic quantum bounds on relaxation (and thermalization) times, examine kinetic theory by taking into account such possible fundamental quantum time scales, find new general equalities connecting semi-classical dynamics and thermodynamics to Plancks constant, and compute current correlation functions. Our analysis suggests that, on average, the extrapolated high temperature dynamical viscosity of general liquids may tend to a value set by the product of the particle number density ${sf n}$ and Plancks constant $h$. We compare this theoretical result with experimental measurements of an ensemble of 23 metallic fluids where this seems to indeed be the case. The extrapolated high temperature viscosity of each of these liquids $eta$ divided (for each respective fluid by its value of ${sf n} h$) veers towards a Gaussian with an ensemble average value that is close to unity up to an error of size $0.6 %$. Inspired by the Eigenstate Thermalization Hypothesis, we suggest a relation between the lowest equilibration temperature to the melting or liquidus temperature and discuss a possible corollary concerning the absence of finite temperature ideal glass transitions. We suggest a general quantum mechanical derivation for the viscosity of glasses at general temperatures. We invoke similar ideas to discuss other transport properties and demonstrate how simple behaviors including resistivity saturation and linear $T$ resistivity may appear very naturally. Our approach suggests that minimal time lags may be present in fluid dynamics.
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Free or integrable theories are usually considered to be too constrained to thermalize. For example, the retarded two-point function of a free field, even in a thermal state, does not decay to zero at long times. On the other hand, the magnetic susceptibility of the critical transverse field Ising is known to thermalize, even though that theory can be mapped by a Jordan-Wigner transformation to that of free fermions. We reconcile these two statements by clarifying under which conditions conserved charges can prevent relaxation at the level of linear response and how such obstruction can be overcome. In particular, we give a necessary condition for the decay of retarded Greens functions. We give explicit examples of composite operators in free theories that nevertheless satisfy that condition and therefore do thermalize. We call this phenomenon the Operator Thermalization Hypothesis as a converse to the Eigenstate Thermalization Hypothesis.
A family of the so-called Maxwell times which arises in the contexto of Higher-Order Generalized Hydrodynamics (also called Mesoscopic Hydro-Thermodynamics) is evidenced. This is done in the framework of a HOGH build within a statistical foundation in terms of a Non-Equilibrium Statistical Ensemble Formalism. It consists in a description in terms of the densities of particles and energy and their fluxes of all orders, with the motion described by a set of coupled nonlinear integro-differential equations involving them. These Maxwell Times have a fundamental role in determining the type of hydrodynamic motion that the system would display in the given condition and constraints. The different types of motion are well described by contractions of the full description done in terms of a reduced number of fluxes up to a certain order.
Boltzmanns ergodic hypothesis furnishes a possible explanation for the emergence of statistical mechanics in the framework of classical physics. In quantum mechanics, the Eigenstate Thermalization Hypothesis (ETH) is instead generally considered as a possible route to thermalization. This is because the notion of ergodicity itself is vague in the quantum world and it is often simply taken as a synonym for thermalization. Here we show, in an elementary way, that when quantum ergodicity is properly defined, it is, in fact, equivalent to ETH. In turn, ergodicity is equivalent to thermalization, thus implying the equivalence of thermalization and ETH. This result previously appeared in [De Palma et al., Phys. Rev. Lett. 115, 220401 (2015)], but becomes particularly clear in the present context. We also show that it is possible to define a classical analogue of ETH which is implicitly assumed to be satisfied when constructing classical statistical mechanics. Classical and quantum statistical mechanics are built according to the familiar standard prescription. This prescription, however, is ontologically justified only in the quantum world.
We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $betall L$. For times $t$ such that $ell/2<t<(L-ell)/2$ the reduced density matrix of a subsystem of length $ell$ is exponentially close to a thermal density matrix. We compute exactly the overlap $cal F$ of the state at time $t$ with the initial state and show that in general it is exponentially suppressed at large $L/beta$. However, for minimal models with $c<1$ (more generally, rational CFTs), at times which are integer multiples of $L/2$ (for periodic boundary conditions, $L$ for open boundary conditions) there are (in general, partial) revivals at which $cal F$ is $O(1)$, leading to an eventual complete revival with ${cal F}=1$. There is also interesting structure at all rational values of $t/L$, related to properties of the CFT under modular transformations. At early times $t!ll!(Lbeta)^{1/2}$ there is a universal decay ${cal F}simexpbig(!-!(pi c/3)Lt^2/beta(beta^2+4t^2)big)$. The effect of an irrelevant non-integrable perturbation of the CFT is to progressively broaden each revival at $t=nL/2$ by an amount $O(n^{1/2})$.
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories (emergent dualities), can be unveiled, and systematically established. Our method relies on the use of morphisms of the bond algebra of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables -which were guessed in the past- can be derived in our formalism. We obtain new self-dualities for four-dimensional Abelian gauge field theories.
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