Classical limit | EPFL Graph Search

The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior. Quantum theory A heuristic postulate called the correspondence principle was introduced to quantum theory by Niels Bohr: in effect it states that some kind of continuity argument should apply to the classical limit of quantum systems as the value of the Planck constant normalized by the action of these systems becomes very small. Often, this is approached through "quasi-classical" techniques (cf. WKB approximation). More rigorously, the mathematical operation involved in classical limits is a group contraction, approximating physical systems where the relevant action is much larger than the reduced Planck constant ħ, so the "deformation parameter" ħ/S can be effectively

Spin-dependent gravitational tail memory in D=4

Biswajit Sahoo

We derive the leading spin-dependent gravitational tail memory, which appears at the second post-Minkowskian order and behaves as u(-2) for large retarded time u. This result follows from the classical soft graviton theorem at order omega In omega as a low-frequency expansion of the gravitational waveform with frequency omega. First, we conjecture the gravitational waveform from the classical limit of the quantum soft graviton theorem up to sub-subleading order in a soft expansion, and then we derive it for a classical scattering process without any reference to the soft graviton theorem. We show that the final result of the gravitational waveform in the direct derivation completely agrees with the conjectured waveform.

AMER PHYSICAL SOC2022

On the Efficiency of Semiclassical and Classical Approximations of Quantum Fidelity in Many-Dimensional Systems

Cesare Mollica

This thesis is focused on classical and semiclassical approximations of a specific quantum time correlation function, the “quantum fidelity.” Namely, we rigorously study the efficiency of a continuous class of algorithms for the evaluation of its classical limit and both the cost and the error of a particular semiclassical approximation of it. In the physics domain, quantum fidelity can be used to study the cross section of inelastic neutron scattering and phenomena like decoherence and irreversibility in NMR experiments. In chemical physics, quantum fidelity can be employed to compute the spectrum of a quantum state, to evaluate the accuracy of quantum dynamics on an approximate potential energy surface, and to verify the importance of nonadiabatic electronic transitions in molecules. Unfortunately, as for any numerical simulation of a quantum dynamical object, many-dimensional calculations of quantum fidelity are extremely expensive computationally. Classical methods, not including any quantum effect, are generally believed to be efficient approximations for the numerical evaluation of large systems’ properties when quantum effects are not important. We prove that, previous to this research, the computational costs of available algorithms for the simulation of classical fidelity increased exponentially with the number of degrees of freedom and we single out, within a continuous family of algorithms, the only one for which the number of trajectories needed for convergence is independent of the system’s dimensionality. Recently a semiclassical method, called “dephasing representation” (DR), has been proposed to approximate quantum fidelity accurately and efficiently. Although semiclassical methods, approximately including all types of quantum effects, are generally more accurate but much less efficient than classical methods, we prove that for the semiclassical DR there exists at least one algorithm for which the number of trajectories needed for convergence is independent of dimensionality and also that this semiclassical algorithm is even faster than the most efficient classical fidelity algorithm previously singled out. Encouraged by the surprising efficiency of the specific semiclassical method, we investigate the error of the DR compared to the quantum benchmark.

EPFL2012

On the Efficiency of Semiclassical and Classical Approximations of Quantum Fidelity in Many-Dimensional Systems

Cesare Mollica

EPFL2012