Search results for "equality"

Dealing with indistinguishable particles and their entanglement

2018

Here we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) which never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated to the standard quantum mechanical treatment of identical particles. The core of this approach is represented by the multiparticle probability amplitude whose structure in terms of single-particle amplitudes we here derive by first principles. To characterise entanglement among the identical particles, this new method utilises the same notions, such as partial trace, adopted for nonidentical ones. We highlight the connection betwee…

The non dissipative damping of the Rabi oscillations as a "which-path" information

2005

Rabi oscillations may be viewed as an interference phenomenon due to a coherent superposition of different quantum paths, like in the Young's two-slit experiment. The inclusion of the atomic external variables causes a non dissipative damping of the Rabi oscillations. More generally, the atomic translational dynamics induces damping in the correlation functions which describe non classical behaviors of the field and internal atomic variables, leading to the separability of these two subsystems. We discuss on the possibility of interpreting this intrinsic decoherence as a "which-way" information effect and we apply to this case a quantitative analysis of the complementarity relation as intro…

Clauser-Horne-Shimony-Holt Bell inequality test in an optomechanical device

2018

We propose here a scheme, based on the measurement of quadrature phase coherence, aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate EPR-like correlations between the quadratures of the output fields of the two cavities, and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality.

Long-Time Preservation of Nonlocal Entanglement

2009

We investigate how nonlocal entanglement, as identified by violations of a Bell inequality, may be preserved during the evolution. Our system consists of two qubits each embedded in a zero-temperature bosonic reservoir evolving independently and initially in an entangled mixed state. We show that the violation of the Bell inequality can be related to the single-qubit population of excited state in such a way that, by appropriately choosing structured environments that give rise to sufficiently high values of population trapping, long-time preservation of nonlocal entanglement can be correspondingly achieved.

HST/WFC3 Confirmation of the Inside-out Growth of Massive Galaxies at 0 < z < 2 and Identification of Their Star-forming Progenitors at z ~ 3

2013

We study the structural evolution of massive galaxies by linking progenitors and descendants at a constant cumulative number density of n_c=1.4x10^{-4} Mpc^{-3} to z~3. Structural parameters were measured by fitting Sersic profiles to high resolution CANDELS HST WFC3 J_{125} and H_{160} imaging in the UKIDSS-UDS at 1<z<3 and ACS I_{814} imaging in COSMOS at 0.25<z<1. At a given redshift, we selected the HST band that most closely samples a common rest-frame wavelength so as to minimize systematics from color gradients in galaxies. At fixed n_c, galaxies grow in stellar mass by a factor of ~3 from z~3 to z~0. The size evolution is complex: galaxies appear roughly constant in size from z~3 to…

Analytic solutions of the Navier-Stokes equations

2001

We consider the time dependent incompressible Navier-Stokes equations on an half plane. For analytic initial data, existence and uniqueness of the solution are proved using the Abstract Cauchy-Kovalevskaya Theorem in Banach spaces. The time interval of existence is proved to be independent of the viscosity.

Self-improving properties of generalized Orlicz-Poincaré inequalities

2006

Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral

2021

Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincar\'{e} inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H\"{o}lder continuous and they satisfy Harnack inequality, the strong maximum principle, and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H\"older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we cons…

Higher Order Sobolev-Type Spaces on the Real Line

2014

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.

Pointwise Hardy inequalities and uniformly fat sets

2008

We prove that it is equivalent for domain in R n \mathbb {R}^n to admit the pointwise p p -Hardy inequality, have uniformly p p -fat complement, or satisfy a uniform inner boundary density condition.