Geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems

Geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems.

Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, such as nanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamical fluctuations of the controlled system. We provide a physically transpare...

A Stochastic Geometric Approach to Quantum Spin Systems

We review some stochastic geometric models that arise from the study of certain quantum spin systems. In these models the fundamental properties of the ground states or equilibrium states of the quantum systems can be given a simple stochastic geometric interpretation. One thus obtains a new class of challenging stochastic geometric problems.

Time Optimal Control in Spin Systems

In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivit...

Time-optimal Control of Spin Systems

A Geometric Approach to the Optimal Control of Nonholonomic Mechanical Systems

In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the controlled dynamics are given by a nonholonomic mechanical system. In our paper, the controlled equations are derived using a basis of vector fields adapted to t...