The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low $T$ up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lamè equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed.
Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity breaking, reassure the H-theorem of global stability [M. Shiino, Phys. Rev. A, Vol 36, pp. 2393-2411 (1987)], and reproduce spatially extended response under alternate source fields.
We study full counting statistics for classical heat transport through anharmonic/nonlinear molecular junctions formed by interacting oscillators. Analytical result of the steady state heat flux for an overdamped anharmonic junction with arbitrary temperature bias is obtained. It is found that the thermal conductance can be expressed in terms of temperature dependent effective force constant. The role of anharmonicity is identified. We also give the general formula for the second cumulant of heat in steady state, as well as the average geometric heat flux when two temperatures are modulated ad…
Motivated by recent experiments on rotating Bose-Einstein condensates, we investigate a rotating, polarized Fermi gas trapped in an anharmonic potential. We apply a semiclassical expansion of the density of states in order to determine how the thermodynamic properties depend on the rotation frequency. The accuracy of the semiclassical approximation is tested and shown to be sufficient for describing typical experiments. At zero temperature, rotating the gas above a given frequency $Ω_{\rm DO}$ leads to a `donut'-shaped cloud which is analogous to the hole found in two-dimensional Bose-Einstein…
We compare two effective phonon theories, which have both been applied recently to study heat conduction in anharmonic lattices. In particular, we study the temperature dependence of the thermal conductivity of the Fermi-Pasta-Ulam model via the Debye formula, showing the equivalence of both approaches. The temperature for the minimum of the thermal conductivity and the corresponding scaling behavior are analytically calculated, which agree well with the result obtained from nonequilibrium simulations. We also give quantum corrections for the thermal conductivity from quantum self-consistent p…
We study heat conduction in one, two and three dimensional anharmonic lattices connected to stochastic Langevin heat baths. The inter-atomic potential of the lattices is double-well type, i.e., $V_{\rm DW}(x)=k_2x^2/2+k_4 x^4/4$ with $k_2<0$ and $k_4>0$. We observe two different temperature regimes of transport: a high-temperature regime where asymptotic length dependence of nonequilibrium steady state heat current is similar to the well-known Fermi-Pasta-Ulam lattices with an inter-atomic potential, $V_{\rm FPU}(x)=k_2x^2/2+k_4 x^4/4$ with $k_2,k_4>0$. A low temperature regime where heat cond…
We consider the problem of heat transport by vibrational modes (conduction) between Langevin thermostats connected by a central device. The latter is anharmonic and can be subject to large temperature differences and thus be out of equilibrium. We develop a self-consistent Green's function formalism to describe high-temperature and non-equilibrium transport, and derive a formula for the heat current for up to quartic anharmonicity (4th-order in the potential energy). We show the importance of including quartic terms in the anharmonic potential in order to properly describe thermal expansion an…
Metastable reverse-phase droplets are calculated by renormalization-group theory by evaluating the magnetization of a droplet under magnetic field, matching the boundary condition with the reverse phase and noting whether the reverse-phase magnetization sustains. The maximal metastable droplet size and the discontinuity across the droplet boundary are thus calculated as a function of field and temperature for the Ising model in three dimensions. The method also yields hysteresis loops for finite systems, as function of temperature and system size.
We study low-temperature magnetization processes in a stacked triangular Ising antiferromagnet by Monte Carlo simulations. In increasing and decreasing magnetic fields we observe multiple steps and hysteresis corresponding to formation of different metastable states. Besides the equidistant threefold splitting of the 1/3 ferrimagnetic plateau, we additionally confirm a fourth plateau in the field-increasing branch and a sizable remanence when the field is decreased to zero. The newly observed plateau only appears at sufficiently low temperature and sufficiently large exchange interaction in th…
The microcanonical effective partition function, constructed from a Feynman-Hibbs potential, is derived using generalized ensemble theory. The form of the effective Hamiltonian is amenable to Monte Carlo simulation techniques and the relevant Metropolis function is presented. Using the derived expression for the microcanonical effective partition function, the low-temperature entropy of a proton in an anharmonic potential is numerically evaluated and compared with the exact quantum mechanical canonical result.
An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. The local anharmonic effects are described by a Morse-like potential and corresponding anharmonic bosons associated with the U(2) algebra. A vibrational high temperature partition function and the related thermodynamic functions are derived in terms of the parameters of the model. The thermal expansion operator is defined and obtained using the renormalized frequency of the model.
We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, th…
Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic…
We study interface thermal resistance (ITR) in a system consisting of two dissimilar anharmonic lattices exemplified by Fermi-Pasta-Ulam (FPU) model and Frenkel-Kontorova (FK) model. It is found that the ITR is asymmetric, namely, it depends on how the temperature gradient is applied. The dependence of the ITR on the coupling constant, temperature, temperature difference, and system size are studied. Possible applications in nanoscale heat management and control are discussed.
We study the finite-temperature transport of electrons coupled to anharmonic local phonons. Our focus is on the high-temperature incoherent regime, where controlled calculations are possible both for weak and strong electron--phonon coupling. At strong coupling, the dynamics is described in terms of a multiple-species gas of small polarons: this emergent `speciation' is driven by energy conservation. We explicitly compute the dc and ac response in this regime. We discuss the breakdown of the polaron picture, and the onset of localization, in the limit where phonons become quasistatic.
Inelastic neutron scattering measurements on silver oxide (Ag$_2$O) with the cuprite structure were performed at temperatures from 40 to 400\,K, and Fourier transform far-infrared spectra were measured from 100 to 300\,K. The measured phonon densities of states and the infrared spectra showed unusually large energy shifts with temperature, and large linewidth broadenings. First principles molecular dynamics (MD) calculations were performed at various temperatures, successfully accounting for the negative thermal expansion (NTE) and local dynamics. Using the Fourier-transformed velocity autocor…
The Mpemba effect refers to systems whose thermal relaxation time is a non-monotonic function of the initial temperature. Thus, a system that is initially hot cools to a bath temperature more quickly than the same system, initially warm. In the special case where the system dynamics can be described by a double-well potential with metastable and stable states, dynamics occurs in two stages: a fast relaxation to local equilibrium followed by a slow equilibration of populations in each coarse-grained state. We have recently observed the Mpemba effect experimentally in such a setting, for a collo…
The dynamics of Davydov-Scott monomer in a thermal bath with higher order amide-site's displacement leads to anharmonic oscillation effect is investigated using full-quantum approach and the Lindblad formulation of master equation. The specific heat is calculated based on the thermodynamic partition function using the path integral method. The temperature dependence of the specific heat is studied. In the model the specific heat anomaly as pointed out in recent works by Ingold et.al is also observed. However it is found that the anomaly occurs at high temperature region, and the anharmonic osc…
In a recent Letter [A. Lapolla and A. Godec, Phys. Rev. Lett. 125, 110602 (2020)], thermal relaxation was observed to occur faster from cold to hot (heating) than from hot to cold (cooling). Here we show that overdamped diffusion in anharmonic potentials generically exhibits both faster heating and faster cooling, depending on the initial temperatures and on the potential's degree of anharmonicity. We draw a relaxation-speed phase diagram that localises the different behaviours in parameter space. In addition to faster-heating and faster-cooling regions, we identify a crossover region in the p…
We compute the first-order correction to the correlation functions of the stationary state of a stochastically forced harmonic chain out of equilibrium when a small on-site anharmonic potential is added. This is achieved by deriving a suitable formula for the covariance matrix of the invariant state. We find that the first-order correction of the heat current does not depend on the size of the system. Second, the temperature profile is linear when the harmonic part of the on-site potential is zero. The sign of the gradient of the profile, however, is opposite to the sign of the temperature dif…
Langevin/Fokker-Planck processes can be immersed in a larger frame by adding fictitious fermion variables. The (super)symmetry of this larger structure has been used to derive Morse theory in an elegant way. The original physical diffusive motion is retained in the zero-fermion subspace. Here we study the subspaces with non-zero fermion number which yield deep information, as well as new computational strategies, for barriers, reaction paths, and unstable states -- even in non-zero temperature situations and when the barriers are of entropic or collective nature, as in the thermodynamic limit.…
We rigorously compute the integrable system for the limiting $(N\rightarrow\infty)$ distribution function of the extreme momentum of $N$ noninteracting fermions when confined to an anharmonic trap $V(q)=q^{2n}$ for $n\in\mathbb{Z}_{\geq 1}$ at positive temperature. More precisely, the edge momentum statistics in the harmonic trap $n=1$ are known to obey the weak asymmetric KPZ crossover law which is realized via the finite temperature Airy kernel determinant or equivalently via a Painlevé-II integro-differential transcendent, cf. \cite{LW,ACQ}. For general $n\geq 2$, a novel higher order finit…
We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this limit, the invariant measure is characterized by a variational principle. We relate the heat flow to the variational principle. The main technical ingredient is an extension of Freidlin-Wentzell theory to a class of degenerate diffusions.
We investigate a class of anharmonic crystals in $d$ dimensions, $d\ge 1$, coupled to both external and internal heat baths of the Ornstein-Uhlenbeck type. The external heat baths, applied at the boundaries in the 1-direction, are at specified, unequal, temperatures $\tlb$ and $\trb$. The temperatures of the internal baths are determined in a self-consistent way by the requirement that there be no net energy exchange with the system in the non-equilibrium stationary state (NESS). We prove the existence of such a stationary self-consistent profile of temperatures for a finite system and show it…
University of Rome La Sapienza（罗马第一大学）；University of Trento（特伦托大学）
Magnesium hydride (MgH$_2$) has been widely studied for effective hydrogen storage. However, its bulk desorption temperature (553 K) is deemed too high for practical applications. Besides doping, a strategy to decrease such reaction energy for releasing hydrogen is the use of MgH$_2$-based nanoparticles (NPs). Here, we investigate first the thermodynamic properties of Mg$_n$H$_{2n}$ NPs ($n<10$) from first-principles, in particular by assessing the anharmonic effects on the enthalpy, entropy and thermal expansion by means of the Stochastic Self Consistent Harmonic Approximation (SSCHA). The la…
