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In a recent letter (PRL 95, 190601 (2005)), T.M. Rocha Filho and coworkers address the very interesting issue of the entropic form to be used for Hamiltonians with long-range interactions. In our opinion the letter misses several points…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
Cosmological time crystals are created when a scalar field moves periodically through phase space in a spatially flat Friedmann-Robertson-Walker spacetime due to the presence of a limit cycle. All such cosmological time crystals in the…
Methods that are devised to achieve reversal of quantum dynamics in time have been named "quatum time mirrors". Such a time mirror can be considered as a generalization of Hahn's spin echo to systems with continuous degrees of freedom. We…
The observation of quantum Hawking radiation and its entanglement in an analogue black hole was recently reported. A subsequent note (arXiv:1609.03803) criticized the study. Version 2 of the note was recently presented. The note suffers…
Time crystals spontaneously break the time translation symmetry, as recently has been frequently reported in quantum systems. Here we describe the observation of classical analogues of both 1+1-dimensional and 2+1-dimensional discrete…
We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp…
We demonstrate that non-convex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. DTCs promise profound applications in precision time-keeping and other…
In this paper I argue that the fundamental aspect of our notion of time is that it defines an order relation, be it a total order relation between configurations of the world or just a partial order relation between events. This position is…
The quantum mechanical wave-particle dualism is analyzed and criticized, in the framework of Reichenbach's concepts of phenomenon and interphenomenon. It is suggested that the dual pictures be de-emphasized in the study of quantum theory,…
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…
We show that recent results on the interaction of causality-respecting particles with particles on closed timelike curves derived in [Phys. Rev. A 82, 062330 (2010)] depend on ambiguous assumption about the form of the state which is…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
A recently introduced discrete formalism allows to solve the problem of time in quantum gravity in a relational manner. Quantum mechanics formulated with a relational time is not exactly unitary and implies a fundamental mechanism for…
Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical…
Our recent paper (arXiv:1701.04298 [quant-ph]) discussed the occurrence of a coupling of centre of mass and internal degrees of freedom for complex quantum systems in non-inertial frames. There, we pointed out that an external force…