Related papers: Duality in Perturbation Theory and the Quantum Adi…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional…
Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry…
Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
We study wave-particle duality by exploring for the first time effects of a quantum object's source. A single photon emitted from a pair of nonlocally entangled two-level atoms is specifically analyzed. Surprisingly, duality is found to be…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear…
We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected,…
A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the…
In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a…
In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show…
The origin of the rather mysterious duality symmetry found in quantum Liouville theory is investigated by considering the Liouville theory as the reduction of a WZW-like theory in which the form of the potential for the Cartan field is not…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…