Related papers: Classical analog of the quantum metric tensor
As is well known, classical systems approximate quantum ones -- but how well? We introduce a definition of a "distance" on classical and quantum phase spaces that offers a measure of their separation. Such a distance scale provides a means…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…
The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which…
We present a general unified approach for the study of quantum thermal machines, including both heat engines and refrigerators, operating under periodic adiabatic driving and in contact with thermal reservoirs kept at different…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it…
In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n^(-1/2) by repeating the measures n times and then averaging. Using quantum…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We introduce the concept of a "classical observable" as an operator with vanishingly small quantum fluctuations on a set of density matrices. It is shown how to construct them for a time evolved pure state. The study of classical…
We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with…
For a quantum observable $A_\hbar$ depending on a parameter $\hbar$ we define the notion ``$A_\hbar$ converges in the classical limit''. The limit is a function on phase space. Convergence is in norm in the sense that $A_\hbar\to0$ is…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…