Related papers: Quantum Analysis and Nonequilibrium Response
We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system…
Linear response theory (LRT) is a key tool in investigating the quantum matter, for quantum systems perturbed by a weak probe, it connects the dynamics of experimental observable with the correlation function of unprobed equilibrium states.…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying…
Quantum coherence and quantum correlations are studied in the strongly interacting system composed of two qubits and an oscillator with the presence of a parametric medium. To analytically solve the system, we employ the adiabatic…
In the framework of Heisenberg-Langevin theory the dynamical and statistical effects arising from the linear interaction of two nondegenerate down-conversion processes are investigated. Using the strong-pumping approximation the analytical…
Conventional wisdom teaches us that the electrical conductivity in a material is the inverse of its resistivity. In this work, we show that when both of these transport coefficients are defined in linear response through the Kubo formulae…
It is known that a semi-classical analysis is not always adequate for atomtronics devices, but that a fully quantum analysis is often necessary to make reliable predictions. While small numbers of atoms at a small number of sites are…
Response functions of quantum systems, such as electron Green's functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Two recent arguments for linear dynamics in quantum theory are critically re-examined. Neither argument is found to be satisfactory as it stands, although an improved version of one of the arguments can in fact be given. This improved…
In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing…
In band insulators, where the Fermi surface is absent, adiabatic transport is allowed only due to the geometry of the Hilbert space. By driving the system at a small but finite frequency $\omega$, transport is still expected to depend…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
An orthodox formulation of quantum mechanics relies on a set of postulates in Hilbert space supplemented with rules to connect it with classical mechanics such as quantisation techniques, correspondence principle, etc. Here we deduce a…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
We investigate quantum dynamical systems defined on a finite dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann…