Related papers: Universal quantum control over non-Hermitian conti…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…
The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework -- a point of ongoing debate in the field. This work addresses this issue by proposing a…
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Error correction is generally demanded in large-scale quantum information processing and quantum computation. We provide here a universal and realtime control strategy to dynamically correct the arbitrary type of errors in the system…
In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…
We introduce time-dependent variational principles to study the non-unitary dynamics of open quantum many-body systems, including dynamics described by the full Lindblad master equation, the non-Hermitian dynamics corresponding to the…
We study dynamical phase transitions occurring in the stationary state of the dynamics of integrable many-body non-hermitian Hamiltonians, which can be either realized as a no-click limit of a stochastic Schr\"{o}dinger equation or using…
For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This…
Recently, synthetic spin-orbit coupling has been introduced into cold-atom systems for more flexible control of the Hamiltonian, which was further made time-varying through two-photon detuning to achieve dynamic control of the cold-atom…
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
Non-unitary quantum mechanics has been used in the past to study irreversibility, dissipation and decay in a variety of physical systems. In this letter, we propose a general scheme to deal with systems governed by non-Hermitian…
Coherent wave control exploits the interference among multiple waves impinging on a system to suppress or enhance outgoing signals based on their relative phase and amplitude. This process inherently requires non-Hermiticity, in order to…
We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space $\cal H$ encoding information decomposes into irreducible sectors and subsystems…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
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…
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of…