Related papers: Real-time dynamics from convex geometry
Quantum dynamics of the density operator in the framework of a single probability vector is analyzed. In this framework quantum states define a proper convex quantum subset in an appropriate simplex. It is showed that the corresponding…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
State-of-the-art quantum simulators permit local temporal control of interactions and midcircuit readout. These capabilities open the way towards the exploration of intriguing nonequilibrium phenomena. We illustrate this with a kinetically…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…
Quantum computing's potential for exponential speedup is fundamentally limited by decoherence, a phenomenon arising from environmental interactions. Non-Hermitian quantum mechanics, particularly $PT$-symmetric systems, offers a novel…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Thermal machines are physical systems designed to convert thermal energy into practical work through cyclic state transformations. A key component in such a machine is a clock-equipped control element that dictates which interaction…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
An abstract formulation of quantum dynamics in the presence of a general set of quantum constraints is developed. Our constructive procedure is such that the relevant projection operator onto the physical Hilbert space is obtained with a…
Quantum dynamics for arbitrary system are traditionally realized by time evolutions of wave functions in Hilbert space and/or density operators in Liouville space. However, the traditional simulations may occasionally turn out to be…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…