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We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently…
We show that the Kaehler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kaehler manifold. By introducing an isometry we explicitly construct the fermionic…
In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, B\"uchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between…
Linear response theory is concerned with the way in which a physical system reacts to a small change in the applied forces. Here we show that quantum mechanics in the Heisenberg representation can be understood as a linear response theory.…
Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism,…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
An index relation $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 1$ is satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a harmonic oscillator. A hermitian phase operator, which inevitably leads to $dim\ ker\…
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the…
The question of how to interpret and compute arrival-time distributions in quantum mechanics remains unsettled, reflecting the longstanding tension between treating time as a quantum observable or as a classical parameter. Most previous…
An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…