We show how to construct, by exploiting adiabatic time and length scale separation between atomistic and continuum mechanics, a multiscale scheme for continuum dynamics free from macroscopic ...constitutive modeling. To do so, we introduce a new set of degrees of freedom that simultaneously represent the macroscopic and the microscopic dynamics, based on a space tessellation. In this new formulation, the dynamics of the macroscopic fields steers the microscopic particle dynamics by producing the conditions under which they evolve and, concurrently, the particle dynamics drives the evolution of the macroscopic fields by providing them with atomistically based constitutive information. Under conditions of adiabatic separation both in time and length scales, it is possible to decimate the tessellating cells and let the macroscopic equations of motion be driven by the time average of the terms coupling them with the microscopic degrees of freedom.
We illustrate how, contrary to common belief, transient Fluctuation Relations (FRs) for systems in constant external magnetic field hold without the inversion of the field. Building on previous work ...providing generalized time-reversal symmetries for systems in parallel external magnetic and electric fields, we observe that the standard proof of these important nonequilibrium properties can be fully reinstated in the presence of net dissipation. This generalizes recent results for the FRs in orthogonal fields-an interesting but less commonly investigated geometry-and enables direct comparison with existing literature. We also present for the first time a numerical demonstration of the validity of the transient FRs with nonzero magnetic field via nonequilibrium molecular dynamics simulations of a realistic model of liquid NaCl.
This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in ...particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths.
We derive the quantum analogues of some recently discovered symmetry relations for time correlation functions in systems subject to a constant magnetic field. The symmetry relations deal with the ...effect of time reversal and do not require—as in the formulations of Casimir and Kubo—that the magnetic field be reversed. It has been anticipated that the same symmetry relations hold for quantum systems. Thus, here we explicitly construct the required symmetry transformations, acting upon the relevant quantum operators, which conserve the Hamiltonian of a system of many interacting spinless particles, under time reversal. Differently from the classical case, parity transformations always reverse the sign of both the coordinates and of the momenta, while time reversal only of the latter. By implementing time reversal in conjunction with ad hoc “incomplete” parity transformations (i.e., transformations that act upon only some of the spatial directions), it is nevertheless possible to achieve the construction of the quantum analogues of the classical maps. The proof that the mentioned symmetry relations apply straightforwardly to quantal time correlation functions is outlined.
We show that quantum time correlation functions including electronically nonadiabatic effects can be computed by using an approach in which their path integral expression is linearized in the ...difference between forward and backward nuclear paths while the electronic component of the amplitude, represented in the mapping formulation, can be computed exactly, leading to classical-like equations of motion for all degrees of freedom. The efficiency of this approach is demonstrated in some simple model applications.
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