Related papers: The solution of the quantum $A_1$ T-system for arb…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
Recent developments in quantum gravity have shown the Lorentzian treatment to be a fruitful approach towards the emergence of macroscopic spacetimes. In this paper, we discuss another related aspect of the Lorentzian treatment: we argue…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space…
In this paper, we discuss the quantum dynamics of a nonlinear system that admits temporally localized solutions at the classical level. We consider a general ordered position-dependent mass Hamiltonian in which the ordering parameters of…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described…
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination,…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
Recent work has revealed a general procedure for incorporating disorder into the semiclassical model of carrier transport, whereby the predictions of quantum linear response theory can be recovered within a quantum kinetic approach based on…
The $A_\infty$ T-system, also called the octahedron recurrence, is a dynamical recurrence relation. It can be realized as mutation in a coefficient-free cluster algebra (Kedem 2008, Di Francesco and Kedem 2009). We define T-systems with…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is based on an original, explicit, and constructive…
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new…
A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…