اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTomograms in the Quantum-Classical transition
100
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The quantum-classical limits for quantum tomograms are studied and compared with the corresponding classical tomograms, using two different definitions for the limit. One is the Planck limit where $hbar to 0$ in all $hbar $-dependent physical observables, and the other is the Ehrenfest limit where $hbar to 0$ while keeping constant the mean value of the energy.The Ehrenfest limit of eigenstate tomograms for a particle in a box and a harmonic oscillatoris shown to agree with the corresponding classical tomograms of phase-space distributions, after a time averaging. The Planck limit of superposition state tomograms of the harmonic oscillator demostrating the decreasing contribution of interferences terms as $hbar to 0$.
قيم البحث
اقرأ أيضاً
The Newton--Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The p
ower dual symmetry is defined by invariance and reciprocity of the action in the form of Hamiltons characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of {the} Green function satisfying the radial Schrodinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb--Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential.
In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonica
l transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-Hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed. The experimental viability of the proposal is studied within a specific context. We suggest that the main theoretical results developed in the present work could be experimentally verified.
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Borns Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the system from the
frame of reference of the subsystem. The unravelling involves a branch dependent Schmidt decomposition of the total state vector. The state in the subsystem frame, the conditioned state, is described by a Poisson process that involves a non-linear deterministic effective Schrodinger equation interspersed with quantum jumps into orthogonal states. We then consider a system whose classical analogue is a generic chaotic system. Although the state spreads out exponentially over phase space, the state in the frame of the subsystem localizes onto a narrow wave packet that follows the classical trajectory due to Ehrenfests Theorem. Quantum jumps occur with a rate that is the order of the effective Lyapunov exponent of the classical chaotic system and imply that the wave packet undergoes random kicks described by the classical Langevin equation of Brownian motion. The implication of the analysis is that this theory can explain in detail how classical mechanics arises from quantum mechanics by using only unitary evolution and Borns Rule applied to a subsystem.
We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Plancks constant $hbar_{eff}equivbeta$ and coupling to the environment, $Gamma$. We study this using stochastic Schrodinger equati
ons, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $beta$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.
We address the pair of conjugated field modes obtained from parametric-downconversion as a convenient system to analyze the quantum-classical transition in the continuous variable regime. We explicitly evaluate intensity correlations, negativity and
entanglement for the system in a thermal state and show that a hierarchy of nonclassicality thresholds naturally emerges in terms of thermal and downconversion photon number. We show that the transition from quantum to classical regime may be tuned by controlling the intensities of the seeds and detected by intensity measurements. Besides, we show that the thresholds are not affected by losses, which only modify the amount of nonclassicality. The multimode case is also analyzed in some detail.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
