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Register a new userEnergy spectrum of a 2D Dirac oscillator in the presence of a constant magnetic field and an antidot potential
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We investigate the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator confined by an antidot potential in the presence of a magnetic field and Aharonov-Bohm flux field. Analytical solutions are obtained and compared with the results of the Schrodinger equation found in the literature. Further, the dependence of the spectrum on the magnetic quantum number and on the repulsive potential is discussed.
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We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Polyas conjecture is not true in the presence of a magnetic field.
We study the impact of a finite magnetic field on the deconfinement phase transition for heavy quarks by computing the fluctuations of the Polyakov loops. It is demonstrated that the explicit Z(3) breaking field increases with the magnetic field, leading to a decrease in the (pseudo) critical temperatures and a shrinking first-order region in the phase diagram. Phenomenological equations that capture the behaviors of the Z(3) breaking field at strong and weak magnetic fields for massive and massless quarks are given. Lastly, we explore the case of dynamical light quarks and demonstrate how an improved constituent quark mass function can enforce the correct magnetic field dependence of the deconfinement temperature in an effective model, as observed in Lattice QCD calculations.
In the present study, the improved screened Kratzer potential (ISKP) is investigated in the presence of external magnetic and Aharanov-Bohm (AB) fields within the framework of non-relativistic quantum mechanics. The Schrodinger equation is solved via the Nikiforov-Uvarov Functional Analysis (NUFA) method and the energy spectra and the corresponding wave function for the ISKP in the presence of external magnetic fields are obtained in a closed form. The obtained energy spectra are used to study three selected diatomic molecules (H2, HCl and LiH). It is observed that the present of the magnetic and AB fields removes the degeneracy for different values of the control parameter. The thermodynamic and magnetic properties of the ISKP in the present of the magnetic and AB fields are also evaluated. The effects of the control potential parameter on the thermodynamic and magnetic properties of the selected diatomic molecules are discussed.
In this note we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm determinant can be exploited in order to compute the modified eigenenergies which differ from those of the harmonic oscillator due to the presence of the Gaussian perturbation. By taking advantage of Wangs results on scalar products of four eigenfunctions of the harmonic oscillator, it is possible to evaluate quite accurately the two lowest-lying eigenvalues as functions of the coupling constant $lambda$.
The coherent states that describe the classical motion of a mechanical oscillator do not have well-defined energy, but are rather quantum superpositions of equally-spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures the mechanical energy with a precision greater than the energy of a single phonon, $hbaromega_text{m}$. One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish different phonon number states by resolvable differences in the atoms transition frequency. Such dispersive measurements have been studied in cavity and circuit quantum electrodynamics where experiments using real and artificial atoms have resolved the photon number states of cavities. Here, we report an experiment where an artificial atom senses the motional energy of a driven nanomechanical oscillator with sufficient sensitivity to resolve the quantization of its energy. To realize this, we build a hybrid platform that integrates nanomechanical piezoelectric resonators with a microwave superconducting qubit on the same chip. We excite phonons with resonant pulses of varying amplitude and probe the resulting excitation spectrum of the qubit to observe phonon-number-dependent frequency shifts $approx 5$ times larger than the qubit linewidth. Our result demonstrates a fully integrated platform for quantum acoustics that combines large couplings, considerable coherence times, and excellent control over the mechanical mode structure. With modest experimental improvements, we expect our approach will make quantum nondemolition measurements of phonons an experimental reality, leading the way to new quantum sensors and information processing approaches that use chip-scale nanomechanical devices.
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