Quantum Variance and Ergodicity for the Baker’s Map
نویسنده
چکیده
We prove a Egorov theorem, or quantum-classical correspondence, for the quantised baker’s map, valid up to the Ehrenfest time. This yields a logarithmic upper bound for the decay of the quantum variance, and, as a corollary, a quantum ergodic theorem for this map.
منابع مشابه
The Approach to Ergodicity in the Quantum Baker’s Map
We study the quantum mechanics of a generalized version of the baker’s map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation functions of observables at different times, and hence control the statistical variance of matrix elements of observables (in the basis of eigenstates of the quant...
متن کاملUsing a quantum computer to investigate quantum chaos
We show that the quantum baker’s map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker’s map could be investigated experimentally on a quantum computer based on only 3 qubits. Since the discovery that a quantum computer can in principle factor large integers in polynomial time [1,2], quantum...
متن کاملOn Quantum - Classical Correspondence for Baker’s Map
Quantum baker‘s map is a model of chaotic system. We study quantum dynamics for the quantum baker’s map. We use the Schack and Caves symbolic description of the quantum baker‘s map. We find an exact expression for the expectation value of the time dependent position operator. A relation between quantum and classical trajectories is investigated. Breakdown of the quantum-classical correspondence...
متن کاملOn the Quantum Baker’s Map and its Unusual Traces
The quantum baker’s map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study of the same revealed some unexpected features which indicated that correction terms of the order of log(h̄) had to be included in the periodic orbit sum. Such ...
متن کاملQuantum ergodicity for graphs related to interval maps
We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakónski et al (J. Phys. A, 34, 9303-9317 (2001)). As observables we take the L functions on the interval. The proof is based on the periodic orbit expansion of a majorant of the quantum variance. Specifically, given a one-dimensional, Lebesguemea...
متن کامل