Ilki Kim

Quantum Brownian motion and the second law of thermodynamics

Abstract.We consider a single harmonic oscillator coupled to a bath at zero temperature. As is well-known, the oscillator then has a higher average energy than that given by its ground state. Here we show analytically that for a damping model with arbitrarily discrete distribution of bath modes and damping models with continuous distributions of bath modes with cut-off frequencies, this excess energy is less than the work needed to couple the system to the bath, therefore, the quantum second law is not violated. On the other hand, the second law may be violated for bath modes without cut-off frequencies, which are, however, physically unrealistic models.

Uncertainty rescued: Bohr's complementarity for composite systems

Abstract Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohrs complementarity thus holds in a much broader sense than anticipated.

Clausius inequality beyond the weak-coupling limit: the quantum Brownian oscillator.

We consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature. We find an exact closed expression for the oscillator density operator. This state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature T*(eff) with an effective mass and an effective spring constant. We derive an effective Clausius inequality deltaQ*(eff)< or =T*(eff)dS , where deltaQ*(eff) is the heat exchanged between the effective (weakly coupled) oscillator and the bath, and S represents a thermal entropy of the effective oscillator, being identical to the von-Neumann entropy of the coupled oscillator. Using this inequality (for a cyclic process in terms of a variation of the coupling strength) we confirm the validity of the second law. For a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant. Then it is never violated. The properly defined Clausius inequality is thus more robust than assumed previously.

Quantum chaos in quantum Turing machines

Abstract We investigate a 2-spin quantum Turing architecture, in which discrete local rotations α m of the Turing head spin alternate with quantum controlled NOT-operations. We demonstrate that a single chaotic parameter input α m leads to a chaotic dynamics in the entire Hilbert-space.

Pattern formation in quantum Turing machines

We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head

Delayed-choice Measurement and Temporal Nonlocality

(\mathrm{pseudospin}S)

Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework

rotating along a closed Turing tape

Field-induced dynamics in the quantum Brownian oscillator: An exact treatment

(M

Quantum chaos in small quantum networks

additional pseudospins). The dynamical evolution of the Bloch vector of S, which can be decomposed into

Moving Quantum Agents in a Finite Environment

{2}^{M}