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This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
We report on the status of the string-inspired world line path integral formalism, a recently developed powerful tool for the reorganisation of standard perturbative amplitudes in quantum field theory. The method is outlined and the present…
We derive two path integral estimators for the derivative of the quantum mechanical potential of mean force (PMF), which may be numerically integrated to yield the PMF. For the first estimator, we perform the differentiation on the exact…
We derive a novel multiple integral representation for a generating function of the $\s^z$-$\s^z$ correlation functions of the spin-$\2$ XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic…
This book provides an introduction to path integral methods and their application to modeling atomistic processes. The book covers both the foundational theory and recently developed simulation techniques. The text provides a self-contained…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
This is a pedagogical review on recent progress in the exact evaluation of physical quantities in interacting quantum systems at finite temperatures. 1D quantum spin chains are discussed in detail as typical examples.
The problem of evaluating heat invariants can be computerized. Geometric symbol calculus of pseudodifferential operators is the main tool of such computerization.
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
A review is given on the thermodynamical structure of bipartite entanglement. By comparing it to the axiomatic formulation of thermodynamics presented by Giles it is shown that for finite dimensional systems the two theories are formally…
We provide an axiomatic framework for Quantum Field Theory at finite temperature which implies the existence of general analyticity properties of the $ n $-point functions; the latter parallel the properties derived from the usual Wightman…
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of…
A recent letter [Lin & Goldman, Phys. Rev. Lett. 106, 127003 (2011)] has presented experimental data in highly disordered thin films, which were interpreted as a quantum phase transition, an intriguing and surprising result for this system.…
We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then…
In recent work by the authors, a connection between Feynman's path integral and Fourier integral operator $\zeta$-functions has been established as a means of regularizing the vacuum expectation values in quantum field theories. However,…
Transport theory is an efficient approach to derive an effective theory for the soft modes of QCD at high temperature. It is known that the leading order operators of this theory can be obtained from (semi-classical) kinetic equations of…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and…
This is a review paper of recent results in the perturbative symmetry approach in the symbolic representation.