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Institute for Advanced Simulation (IAS)
Some fundamental questions in statistical mechanics such as under which conditions a system coupled to a reservoir equilibrates and how the canonical distribution emerges from the interaction between the system and the reservoir, have only been partially resolved. Roughly and more generally speaking one could say that the main unresolved question is how the basic equations of physics, which are all deterministic and timereversible, can give rise to the timeirreversible (thermodynamic) phenomena that we observe.
As well for classical as quantum systems it is wellknown that if the interaction between a system and a much larger reservoir having a large number of degrees of freedom and a dense distribution of energy levels, is weak, the system is described by a canonical ensemble when the composite system is described by the microcanonical ensemble with a given total energy.
In the case of quantum systems, it has recently been shown that the microcanonical mixed state for the composite system is not a required starting point for the system to be described by a canonical ensemble, but that the composite system being initially in a randomly picked pure state is sufficient.
Using approximationfree simulation methods we have studied the equilibration of systems of 4 spin1/2 particles coupled to a reservoir of 18 to 31 spin1/2 particles, both the system and the reservoir being described by general quantum spin1/2 Hamiltonians. The initial state of the composite system was taken to be a product state of a pure state of the system and a pure state of the reservoir, representing the reservoir at a given temperature in the canonical ensemble. We solved the timedependent Schrödinger equation, governing the timeevolution of the closed composite quantum system, numerically and then analyzed the behavior of the reduced density matrix of the system, obtained by tracing out the degrees of freedom of the reservoir. As a function of time we have calculated the variance of the set of eigenvalues of the reduced density matrix, the entropy, the degree of decoherence of the system and the difference between the reduced density matrix and the canonical distribution. Our simulation results show that, independent of the strength of the interaction between the system and the reservoir and the initial temperature of the reservoir, the system evolves to a stationary state of which the properties strongly depend on the initial temperature of the reservoir. This equilibration is remarkable given the relative small size of the reservoir, since usually in equilibration studies the hypothesis of having a large reservoir is essential. We show that for sufficiently large initial temperatures of the reservoir, the stationary state of the system is represented by a canonical ensemble density matrix at some finite effective temperature. For decreasing temperatures, the reduced density matrix of the system deviates from the canonical density matrix. The deviation increases for decreasing values of the interaction strength between the system and the reservoir.
Molecular magnets are generally considered as potential candidates for realizing scalable quantum information processing. Crucial for quantum information applications is that the qubits (i.e. spin1/2 particles) in these magnets exhibit coherence over a sufficiently long period of time. For instance, the V15 molecular magnet is an assembly of 15 spin1/2 electrons that has been shown to display Rabi oscillations, indicating that it may be a suitable system for obtaining long coherence times.
Experiments indicate that the conventional Bloch equations are insufficient to fully describe the quantum dynamical response of these systems to applied fields, which is essential for quantum information applications. For instance, empirically one finds that the observed coherence time depends on the applied microwave power, among other things. This observation has been associated with adhoc stochastic noise in the applied microwave field but the origin of this noise remains elusive.
We study this problem starting from a realistic model of the magnetic properties of a collection of molecular magnets, including local anisotropic fields, dipolar interactions etc. By solving the timedependent Schrödinger equation of the interacting spin system directly and by adopting the same procedure as used in pulsed electronspinresonance experiments, we can follow the time evolution of the spins explicitly and extract the information that is necessary to disentangle the different processes that give rise to the observed phenomena. Note that in the simulation model it is essential to account for the (longrange) dipoledipole interactions that are always present in real magnetic materials.
Journal Article
Scaling of diffusion constants in the spin$\frac{1}{2}$ XX ladder
Physical review / B 90(9), 094417 (2014) [10.1103/PhysRevB.90.094417]
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Macroscopically deterministic Markovian thermalization in finite quantum spin systems
Physical review / E 89(1), 012131 (2014) [10.1103/PhysRevE.89.012131]
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Contribution to a book/Contribution to a book
Data analysis of EinsteinPodolskyRosenBohm laboratory experiments
Proc. of SPIE
SPIE Optical Engineering + Applications, San DiegoSan Diego, California, 26 Aug 2013  29 Aug 2013
88321N1  88321N11 (2013) [10.1117/12.2021860] special issue: "The Nature of Light: What are Photons? V"
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Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness
Physical review / A 87(2), 022117 (2013) [10.1103/PhysRevA.87.022117]
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Journal Article
Equilibration and thermalization of classical systems
New journal of physics 15(3), 033009 (2013) [10.1088/13672630/15/3/033009]
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An Efficient Algorithm for Simulating the RealTime Quantum Dynamics of a Single Spin1/2 Coupled to Specific Spin1/2 Baths
Journal of physics / Conference Series 402, 012019 (2012) [10.1088/17426596/402/1/012019]
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Dynamics of a Single Spin1/2 Coupled to x and ySpin Baths: Algorithm and Results
Physics procedia 34, 9099 (2012) [10.1016/j.phpro.2012.05.015]
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Journal Article
Quantum simulations and experiments on Rabi oscillations of spin qubits: Intrinsic vs extrinsic damping
Physical review / B 85, 014408 (2012) [10.1103/PhysRevB.85.014408]
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Approach to Equilibrium in Nanoscale Systems at Finite Temperature
Journal of the Physical Society of Japan 79, 124005 (2010) [10.1143/JPSJ.79.124005]
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