Related papers: Computing characteristic functions of quantum work…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
The ``problem of time'' has been a pressing issue in quantum gravity for some time. To help understand this problem, Rovelli proposed a model of a two harmonic oscillators system where one of the oscillators can be thought of as a ``clock''…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
We extend the notion of quantum blob studied in previous work to excited states of the generalized harmonic oscillator in n dimensions. This extension is made possible by Fermi's observation in 1930 that the state of a quantum system may be…
We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
Here we prove that the classical (respectively, quantum) system, consisting of a particle moving in a static electromagnetic field, is canonically (respectively, unitarily) equivalent to a harmonic oscillator perturbed by a spatially…
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or…
By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for…
The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We extend the stochastic quantization method recently developed by Haba and Kleinert to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation and computing. However, a full characterization of multimode quantum states requires a number of…
Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator…