相关论文: Phase Operator Problem and Macroscopic Extension o…

A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…

The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the…

Geometric phases play a fundamental role in understanding quantum topology, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop…

An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…

In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schr\"{o}dinger representation (working often with the innovative and heuristically productive concept of ${\cal PT}-$symmetry), it is demonstrated…

Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…

The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…

Time flow has been embodied in time-dependent Schroedinger equation representing one of the foundations of quantum mechanics. Pauli's criticism (1933) has, however, indicated that the assumptions concerning representation Hilbert space have…

We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and…

We consider the problem of determining the spatial phase profile of a single-mode electromagnetic field. Our attention is on input states that are a statistical mixture of displaced and squeezed number states, a superset of Gaussian states.…

Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…

Quantum phase estimation is a cornerstone in quantum algorithm design, allowing for the inference of eigenvalues of exponentially-large sparse matrices.The maximum rate at which these eigenvalues may be learned, --known as the Heisenberg…

This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…

In their Erratum [Phys. Rev. Lett. {\bf 92}, 119902 (2004), quant-ph/0208076], written in reaction to [quant-ph/0310164], Bender, Brody and Jones propose a revised definition for a physical observable in PT-symmetric quantum mechanics. We…

Within the quantum phase representation we derive Heisenberg limits, in closed form, for N00N states and two other classes of states that can perform better in terms of local performance metrics relevant for multiply-peaked distributions.…

Operators in quantum mechanics - either observables, density or evolution operators, unitary or not - can be represented by c-numbers in operator bases. The position and momentum bases are in one to one correspondence with lagrangian planes…

We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the…

Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…