Quantum Irreversibility of Energy Spreading

– The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One (”Loschmidt echo”) is related to ”time reversal”, while the other is related to ”driving reversal”. In the latter context we define the time of maximum return (”compensation time”) which generalizes the notion of ”echo time”. Non-perturbative features manifest themselves in the energy spreading process. This is demonstrated for the prototype random-matrix Wigner model, where the compensation time and the system response exhibit a non-universal scaling behavior. Quantum Irreversibility (QI) [1] is a subject of a recent intensive research activity due to its relevance to quantum computing [2]. It turns out that the analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two different notions of ”irreversibility”. One is based on the ”piston model” paradigm (PMP), while the other is based on the ”ice cube in a cup of hot water” paradigm (ICP). The latter notion has been adopted by the recent literature [1, 2], and it is related to the studies of dephasing due to the interaction with chaotic degrees of freedom [3]. The PMP on the other hand has direct relevance to our recent studies [4] of the (non-perturbative) response of driven chaotic mesoscopic systems. In the PMP case we say that a process is reversible if it is possible to ”undo” it. Consider a gas inside a cylinder with a piston. Let us shift the piston inside. Due to the compression the gas is heated up. Can we undo the ”heating” simply by shifting the piston outside, back to its original position? If the answer is ”yes”, as in the case of strictly adiabatic process, then the process is said to be reversible. In the ICP case we consider the melting process of an ice cube. Let us assume that after some time we reverse the velocities of all the molecules. If the external conditions are kept strictly the same, we expect the ice-cube to re-emerge out of the water. In practice the external conditions (fields) are not exactly the same, and as a result we have what looks like irreversibility. It is also essential to define precisely what is the measure for QI. The prevailing possibility is to take the survival probability as a measure [1]. Another possibility is to take the energy spreading as a measure. (The energy spreading is defined as the square root of the energy variance.) The latter definition goes well with the PMP, and it has a well defined classical limit.