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A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the…
In a recent paper [1] (also at http://lanl.arxiv.org/abs/0803.3721), I made several critical remarks on a 'Hermitian time operator' proposed by Galapon [2] (also at http://lanl.arxiv.org/abs/quant-ph/0111061). Galapon has correctly pointed…
The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental…
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in…
In order to see the behavior of $\imath$canonical bases at $q = \infty$, we introduce the notion of $\imath$crystals associated to an $\imath$quantum group of certain quasi-split type. The theory of $\imath$crystals clarifies why…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body…
We discuss the possibility of making a quasi time crystal. A simple two-state model is studied to clarify our definition. In a superposition of the ground state and the excited state and the probability of observation varies periodically in…
We strongly disagree with a number of statements by Dolin{\v{s}}ek et al. about phason dynamics in quasicrystals (QCs).
The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
We investigate the time neutral formulation of quantum cosmology of Gell-Mann and Hartle. In particular we study the proposal discussed by them that our Universe corresponds to the time symmetric decoherence functional with initial and…
The phenomenon of quantum tunneling remains a fascinating and enigmatic one, defying classical notions of particle behavior. This paper presents a novel theoretical investigation of the tunneling phenomenon, from the viewpoint of Hartman…
In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental time-evolution parameter) and the…
Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under…
I argue that a single driven quantum Van der Pol oscillator should not be considered a dissipative time crystal, contrary to previous claims. In particular, I show that its phase is prone to randomly drift when considering dephasing or…
This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)).
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…