Related papers: Duality and Scaling in Quantum Mechanics
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…
Previous work developed a space-time metric with two cosmological scales; one that conveniently describes the classical evolution of the dynamics, and the other describing a scale associated with macroscopic quantum aspects like vacuum…
Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schr\"odinger equation, which…
We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic…
The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.
Motivated for the fault tolerant quantum computation, quantum gate by adiabatic geometric phase shift is extensively investigated. In this paper, we demonstrate the nonadiabatic scheme for the geometric phase shift and conditional geometric…
We present exact quantum solutions for a noncommutative, multidimensional cosmological model and show that stabilization of extra dimensions sets in with the introduction of noncommutativity between the scale factors. An interpretation is…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
In this paper we construct a noncommutative space of ``pointed Drinfeld modules'' that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
It is shown with the help of skew-symmetric forms that the mathematical physics equations, on which no additional conditions are imposed, have quantum properties. And this is due to the integrability properties of differential equations,…
In the present work we recall and extend the results of previous work concerning the time evolution of open quantum systems. We show how general properties of such systems are related to their structure properties, those of their…
We discuss the emergence of time in quantum gravity, and ask whether time is always "something that flows"'. We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time…
We study the effect of an external harmonic trapping potential on an outcome of the non-adiabatic quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 atomic condensate. Previously, we demonstrated that…