Search results for "Statistical and Nonlinear Physics"
showing 10 items of 896 documents
Weak commutation relations of unbounded operators and applications
2011
Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.
Singularity formation for Prandtl’s equations
2009
Abstract We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen’s singularity as a cubic root singularity. We introduce a class of initial data, uniformly bounded in H 1 , which have a dipole singularity in the complex plane. These data lead to a solution blow-up whose time can be made arbitrarily short within the class. This is numerical evidence of the ill-posedness of the Prandtl equations in H 1 . The presence of a small viscosity in the streamwise direction changes the behavior of the singularities. They stabilize at a distanc…
Determining a Random Schrödinger Operator : Both Potential and Source are Random
2020
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…
An example of cancellation of infinities in the star-quantization of fields
1993
Within the *-quantization framework, it is shown how to remove some of the divergences occurring in theλo 2 4 -theory by introducing aλ-dependent *-product cohomologically equivalent to the normal *-product.
Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation
2019
International audience; The inverse scattering approach for the defocusing Davey–Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
Appearances of pseudo-bosons from Black-Scholes equation
2016
It is a well known fact that the Black-Scholes equation admits an alternative representation as a Schr\"odinger equation expressed in terms of a non self-adjoint hamiltonian. We show how {\em pseudo-bosons}, linear or not, naturally arise in this context, and how they can be used in the computation of the pricing kernel.
Robust entanglement preparation against noise by controlling spatial indistinguishability
2019
Initialization of composite quantum systems into highly entangled states is usually a must to allow their use for quantum technologies. However, the presence of unavoidable noise in the preparation stage makes the system state mixed, thus limiting the possibility of achieving this goal. Here we address this problem in the context of identical particle systems. We define the entanglement of formation for an arbitrary state of two identical qubits within the operational framework of spatially localized operations and classical communication (sLOCC). We then introduce an entropic measure of spatial indistinguishability under sLOCC as an information resource. We show that spatial indistinguisha…
Energy-efficient quantum computing
2016
In the near future, a major challenge in quantum computing is to scale up robust qubit prototypes to practical problem sizes and to implement comprehensive error correction for computational precision. Due to inevitable quantum uncertainties in resonant control pulses, increasing the precision of quantum gates comes with the expense of increased energy consumption. Consequently, the power dissipated in the vicinity of the processor in a well-working large-scale quantum computer seems unacceptably large in typical systems requiring low operation temperatures. Here, we introduce a method for qubit driving and show that it serves to decrease the single-qubit gate error without increasing the a…
Acoustic spectral hole-burning in a two-level system ensemble
2020
AbstractMicroscopic two-level system (TLS) defects at dielectric surfaces and interfaces are among the dominant sources of loss in superconducting quantum circuits, and their properties have been extensively probed using superconducting resonators and qubits. We report on spectroscopy of TLSs coupling to the strain field in a surface acoustic wave (SAW) resonator. The narrow free spectral range of the resonator allows for two-tone spectroscopy where a strong pump is applied at one resonance, while a weak signal is used to probe a different mode. We map the spectral hole burnt by the pump tone as a function of frequency and extract parameters of the TLS ensemble. Our results suggest that det…
Intertwining operators between different Hilbert spaces: connection with frames
2009
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.