Related papers: Classical and Quantum Dilogarithm Identities
A classical fluid splitter produces the same patterns of energy redistribution as a Stern-Gerlach quantum device, with rotationally invariant coefficients of correlation between molecular paths. Alternative settings express a cosine squared…
The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…
In contrast to the intuitively plausible assumption of local realism, entangled particles, even when isolated, are not allowed to possess definite properties in their own right, as quantitatively expressed by violations of Bell's…
In this paper, we study the relations between groups related to cluster automorphism groups which are defined by Assem, Schiffler and Shamchenko in \cite{ASS}. We establish the relationship among (strict) direct cluster automorphism groups…
In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…
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 quantal algebra combines classical and quantum mechanics into an abstract structurally unified structure. The structure uses two products: one symmetric and one anti-symmetric. The local structure of spacetime is contained in the…
In this paper, we show that the infinitesimal dilogarithm and Kontsevich's one-and-a-half logarithm function satisfies the identities which result from periods in cluster patterns. We also prove that these cluster identities are a…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…
The dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
This is the second part of a three-part overview, in which we derive the category-theoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part…
We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
We use an alternative approach to show that quantum entanglement-like correlations cannot be reproduced for any classical protocol. In our proposal, quantum geometric restrictions are impose over the physical system related to the existence…
In this article, we introduce the notion of cluster automorphism of a given cluster algebra as a $\ZZ$-automorphism of the cluster algebra that sends a cluster to another and commutes with mutations. We study the group of cluster…
For a locally compact quantum group $\mathbb{G}$ we define its center, $\mathscr{Z}(\mathbb{G})$, and its quantum group of inner automorphisms, $\mathrm{Inn}(\mathbb{G})$. We show that one obtains a natural isomorphism between…
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…