相关论文: An Algebraic PT-Symmetric Quantum Theory with a Ma…
We construct a Heisenberg-like algebra for the one dimensional quantum free Klein-Gordon equation defined on the interval of the real line of length $L$. Using the realization of the ladder operators of this type Heisenberg algebra in terms…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…
Pseudo-Hermitian (including $\mathcal{PT}$-symmetric) field theories support phenomenology that cannot be replicated in standard Hermitian theories. We describe a concrete example in which the vortex solutions that are realised in a…
In an attempt to generalize general relativity, we propose a new Hermitian theory of gravity. Space-time is generalized to space-time-momentum-energy and both the principles of general covariance and equivalence are extended. The theory is…
We explain why the main conclusion of Bender et al, hep-th/0511229 [J. Phys. A 39 (2006) 1657] regarding the practical superiority of the non-Hermitian description of PT-symmetric quantum systems over their Hermitian description is not…
We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we…
Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…
The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction with the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the…
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…
We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We…
Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly…
This note summarises recent progress in the formulation of flavour mixing and oscillations in pseudo-Hermitian quantum theories with non-Hermitian mass mixing matrices. Such non-Hermitian quantum theories are made viable by the existence of…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian $\cal PT$-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state $|\psi_i\rangle$…
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…