ترغب بنشر مسار تعليمي؟ اضغط هنا

Ehrenfest principle and unitary dynamics of quantum-classical systems with general potential interaction

115   0   0.0 ( 0 )
 نشر من قبل Buric Nikola
 تاريخ النشر 2014
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between classical and quantum ones. We solved the problem of unitary description of two interpolating systems with general potential interaction. The general solution is used to show that with arbitrary potential interaction between the two interpolating systems the evolution of the so called unobservable variables is decoupled from that of the observable ones if and only if the interpolation parameters in the two interpolating systems are equal.



قيم البحث

اقرأ أيضاً

We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that depends only on the underlying quantum circuit. Finally, we use our formalization of quantum circuits to state precisely and prove the principle of deferred measurements.
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum stabilizer state s and product states, thereby generalizing mappings for some specific models established in [Phys. Rev. Lett. 98, 117207 (2007)]. For Ising- and Potts-type models with and without external magnetic field, we show how the entanglement features of the corresponding stabilizer states are related to the interaction pattern of the classical model, while the choice of product states encodes the details of interaction. These mappings establish a link between the fields of classical statistical mechanics and quantum information theory, which we utilize to transfer techniques and methods developed in one field to gain insight into the other. For example, we use quantum information techniques to recover well known duality relations and local symmetries of classical models in a simple way, and provide new classical simulation methods to simulate certain types of classical spin models. We show that in this way all inhomogeneous models of q-dimensional spins with pairwise interaction pattern specified by a graph of bounded tree-width can be simulated efficiently. Finally, we show relations between classical spin models and measurement-based quantum computation.
158 - J. Novotny , G. Alber , I. Jex 2009
We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimens ional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations.
We show that in the few-excitation regime the classical and quantum time-evolution of the inhomogeneous Dicke model for N two-level systems coupled to a single boson mode agree for N>>1. In the presence of a single excitation only, the leading term i n an 1/N-expansion of the classical equations of motion reproduces the result of the Schroedinger equation. For a small number of excitations, the numerical solutions of the classical and quantum problems become equal for N sufficiently large. By solving the Schroedinger equation exactly for two excitations and a particular inhomogeneity we obtain 1/N-corrections which lead to a significant difference between the classical and quantum solutions at a new time scale which we identify as an Ehrenferst time, given by tau_E=sqrt{N<g^2>}, where sqrt{<g^2>} is an effective coupling strength between the two-level systems and the boson.
We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehr enfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field, through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum-classical (mean field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا