arXiv subjects

Jiri Vanicek

Publications and source records attributed to Jiri Vanicek.

28 records · Page 2Linked to original sources

arXiv2009

Path integral evaluation of equilibrium isotope effects

A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of 60 at 500 K. We describe the implementation of the methodology in the molecular dynamics package Amber 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation, and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering and coworkers, confirming the accuracy of the most recent measurement on 2,4,6,7,9-pentamethyl-5-(5,5-$^2$H$_2$)methylene-11,11a-dihydro-12H-naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2-methyl-10-(10,10-$^2$H$_2$)methylenebicyclo[4.4.0]dec-1-ene.

physics.chem-ph↗

arXiv2009

Efficient evaluation of accuracy of molecular quantum dynamics using dephasing representation

Ab initio methods for electronic structure of molecules have reached a satisfactory accuracy for calculation of static properties, but remain too expensive for quantum dynamical calculations. We propose an efficient semiclassical method for evaluating the accuracy of a lower level quantum dynamics, as compared to a higher level quantum dynamics, without having to perform any quantum dynamics. The method is based on dephasing representation of quantum fidelity and its feasibility is demonstrated on the photodissociation dynamics of CO2. We suggest how to implement the method in existing molecular dynamics codes and describe a simple test of its applicability.

physics.chem-ph↗

arXiv2006

Path integral evaluation of the kinetic isotope effects based on the quantum instanton approximation

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral Monte-Carlo evaluation of relevant thermodynamic quantities. The central ingredients of the method are the Monte-Carlo estimators for the logarithmic derivatives of the partition function and the delta-delta correlation function. Several alternative estimators for these quantities are described here and their merits are compared on the benchmark hydrogen-exchange reaction, H+H_2->H_2+H on the Truhlar-Kuppermann potential energy surface. Finally, a qualitative discussion of issues arising in many-dimensional systems is provided.

physics.chem-ph↗

arXiv2005

Dephasing representation of quantum fidelity for general pure and mixed states

General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for physical perturbations and for numerical errors. It is shown how the general expression reduces to the special forms for position and momentum states and for wave packets localized in position or momentum. The superiority of the general over the specialized forms is explained and supported by numerical tests for wave packets, non-local pure states, and for simple and random mixed states. The tests are done in non-universal regimes in mixed phase space where detailed features of fidelity are important. Although semiclassically motivated, present approach is valid for abstract systems with a finite Hilbert basis provided that the discrete Wigner transform is used. This makes the method applicable, via a phase space approach, e. g., to problems of quantum computation.

quant-ph↗

arXiv2004

Dephasing representation: Unified semiclassical framework for fidelity decay

This paper presents a unified semiclassical framework for five regimes of quantum fidelity decay and conjectures a new universal regime. The theory is based solely on the statistics of actions in the dephasing representation. Counterintuitively, in this representation, all of the decay is due to interference and none due to the decay of classical overlaps. Both rigorous and numerical support of the theory is provided.

quant-ph↗

arXiv2004

Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions

Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is used to find a unique semiclassical representation without the Van Vleck determinant, applicable to a large class of correlation functions expressible as quantum fidelity. As in the Feynman path integral formulation of quantum mechanics, all contributing trajectories have the same amplitude: that is why it is denoted the ``dephasing representation.'' By relating the present approach to the problem of existence of true trajectories near numerically-computed chaotic trajectories, the approximation is made rigorous for any system in which the shadowing theorem holds. Numerical implementation only requires computing actions along the unperturbed trajectories and not finding the shadowing trajectories. While semiclassical linear-response theory was used before in quasi-integrable and chaotic systems, here its validity is justified in the most generic, mixed systems. Dephasing representation appears to be a rare practical method to calculate quantum correlation functions in nonuniversal regimes in many-dimensional systems where exact quantum calculations are impossible.

quant-ph↗

arXiv2003

Semiclassical evaluation of quantum fidelity

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 10^70 semiclassical contributions. Remarkably, it also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation (CPA) and show that within this approximation, the so-called ``diagonal approximation'' is automatic and does not require ensemble averaging.

quant-ph↗

arXiv2003

The survival probability and the local density of states for one-dimensional Hamiltonian systems

For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes, and to the observation that semiclassical tools are useful in the latter case. We discuss what is "left" from this theory in the case of one-dimensional systems. We demonstrate that the remarkably accurate {\em uniform} semiclassical approximation captures the physics of {\em all} the different regimes, though it cannot take into account the effect of strong localization.

quant-ph↗

arXiv2002

Uniform semiclassical wave function for coherent 2D electron flow

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The formation of branches has been explained by classical arguments, but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work for a continuous-time model as well.

nlin.CD↗

arXiv2001

A new class of semiclassical wave function uniformizations

We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy. We give several working examples to illustrate the theory presented here.

nlin.CD↗