相关论文: Sheaf Cohomology and Geometrical Approach to EPR N…
We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to that used in the bi-metric approach to massive gravity, and apply it to describe abelian anisotropic FQH…
Some of the strategies which have been put forward in order to deal with the inconsistency between quantum mechanics and special relativity are examined. The EPR correlations are discussed as a simple example of quantum mechanical…
The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables…
Various aspects of nonlocality of a quantum wave are discussed. In particular, the question of the possibility of extracting information about the relative phase in a quantum wave is analyzed. It is argued that there is a profound…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
We study the geometry of the Quot scheme $\mathrm{Quot}^l_{S}(\mathcal{E})$ of length $l$ coherent sheaf quotients of a locally free sheaf $\mathcal{E}$ on a smooth projective surface $\mathrm{S}$. In particular, we investigate the nature…
The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and…
The EPR paradox is known as an interpretive problem, as well as a technical discovery in quantum mechanics. It defined the basic features of two-quantum entanglement, as needed to study the relationships between two non-commuting variables.…
Although the original EPR paradox was formulated in terms of position and momentum, most studies of these phenomena have focused on measurement scenarios with only a discrete number of possible measurement outcomes. Here, we present a…
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent,…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
The sheaf-theoretic structure is useful in classifying no-go theorems related to non-locality and contextuality. It provides a new point of view different from conventional formularization of quantum mechanics. First, we examine a…
The possible nature of the nonlinear evolution of quantum systems is explored from the point of view of nonlocal effects under the conditions of EPR paradox. It is shown that both stochastic and deterministic mechanisms of nonlocal…
As shown in the \emph{EPR} paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics is a non-local Theory. The Bell theorem and the successive experiments ruled out the possibility of explaining quantum correlations using only local…
We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite…
By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is…
One of the authors has recently propounded an SR (semantic realism) model which shows, circumventing known no-go theorems, that an objective (noncontextual, hence local) interpretation of quantum mechanics (QM) is possible. We consider here…
The experimental results that test Bell's inequality have found strong evidence suggesting that there are nonlocal aspects in nature. Evidently, these nonlocal effects, which concern spacelike separated regions, create an enormous tension…
We examine local cohomology in the setting of valuation rings. The novelty of this investigation stems from the fact that valuation rings are usually non-Noetherian, whereas local cohomology has been extensively developed mostly in a…