Related papers: Effective approach to the problem of time: general…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
This Series of Articles provides a local resolution of this major longstanding foundational problem between QM and GR, or, more generally, between Background Dependent and Background Independent Physics. We focus on the classical version;…
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories.…
The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic…
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical…
The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical…
Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory…
Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures…
Intrinsic time quantum geometrodynamics resolved `the problem of time' and bridged the deep divide between quantum mechanics and canonical quantum gravity with a Schrodinger equation which describes evolution in intrinsic time variable. In…
We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems from fully quantum dynamics. In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and…
The Problem of Time is that `time' in each of ordinary quantum theory and general relativity are mutually incompatible notions. This causes difficulties in trying to put these two theories together to form a theory of Quantum Gravity. The…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization. In particular, it is impossible to derive proper-time effective equations…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
It is demonstrated here that local dynamics have the ability to strongly modify the entangling power of unitary quantum gates acting on a composite system. The scenario is common to numerous physical systems, in which the time evolution…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
We consider the ability of local quantum dynamics to solve the energy matching problem: given an instance of a classical optimization problem and a low energy state, find another macroscopically distinct low energy state. Energy matching is…
The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima,…
We introduce a new discrete-time variational principle inspired by the quantum clock originally proposed by Feynman, and use it to write down quantum evolution as a ground state eigenvalue problem. The construction allows one to apply…