The dynamic properties of a biased two-level system in contact with a dissipative bath are studied in the weak coupling limit using a resolvent expansion method. The theory yields consistent results at low temperatures, a regime in which the widely used dilute bounce gas approximation (DBGA) to an underlying functional integral expression breaks down. The present results are however equivalent to a recently adapted functional integral technique that goes beyond the DBGA. The calculated expressions are relevant for analyzing the neutron scattering data on tunneling of light interstitials, e.g., hydrogen, in metals, at very low temperatures.

We study the dissipative, classical dynamics of a charged particle in the presence of a magnetic field. Two stochastic models are employed, and a comparative analysis is made, one based on diffusion processes and the other on jump processes. In the literature on collision-broadening of spectral lines, these processes go under the epithet of weak-collision model and Boltzmann-Lorentz model, respectively. We apply our model calculation to investigate the effect of magnetic field on the collision-broadened spectral lines, when the emitter carries an electrical charge. The spectral lines show narrowing as the magnetic field is increased, the narrowing being sharper in the Boltzmann-Lorentz model than in the weak collision model.

We study the quantum Brownian motion of a charged particle in the presence of a magnetic field. From the explicit solution of a quantum Langevin equation we calculate quantities such as the velocity correlation function and the mean-squared displacement. Our calculated expressions contain as special cases the motion of aclassical particle in a magnetic field and that of afree (but quantum) particle, in a dissipative environment.

We present an ‘overview’ of coherence-to-decoherence transition in certain selected problems of condensed matter physics. Our treatment is based on a subsystem-plus-environment approach. All the examples chosen in this paper have one thing in common — the environmental degrees of freedom are taken to be bosonic and their spectral density of excitations is assumed to be ‘ohmic’. The examples are drawn from a variety of phenomena in condensed matter physics involving, for instance, quantum diffusion of hydrogen in metals, Landau diamagnetism and c-axis transport in high T_c superconductors.

We revisit the Anderson-Hasegawa double-exchange model and critically examine its exact solution when the core spins are treated quantum mechanically. We show that the quantum effects, in the presence of an additional superexchange interaction between the core spins, yield a term, the significance of which has been hitherto ignored. The importance of this term is further assessed by numerically exact computation for a four-spin system.

We investigate the solvability of a variety of well-known problems in lattice statistical mechanics. We provide a new numerical procedure which enables one to conjecture whether the solution falls into a class of functions called differentiably finite functions. Almost all solved problems fall into this class. The fact that one can conjecture whether a given problem is or is not 𝐷-finite then informs one as to whether the solution is likely to be tractable or not. We also show how, for certain problems, it is possible to prove that the solutions are not 𝐷-finite, based on the work of Rechnitzer $[1–3]$.

This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a `Kapitza Window' over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.

The qubit (or a system of two quantum dots) has become a standard paradigm for studying quantum information processes. Our focus is decoherence due to interaction of the qubit with its environment, leading to noise. We consider quantum noise generated by a dissipative quantum bath. A detailed comparative study with the results for a classical noise source such as generated by a telegraph process, enebles us to set limits on the pplicability of this process $\nu is à \nu is$ its quantum counterpart, as well as lend handle on the parameters that can be tuned for analysing decoherence. Both Ohmic and non-Ohmic dissipations are treated and appropriate limits are analysed for facilitating comparison with the telegraph process.

We give a pedagogical overview of exciting quantum phenomena that are unique to two-dimensional electron solids. The uniqueness arises from the role of the quantum phase that influences various remarkable attributes such as the relativistic Rashba interaction, the Berry curvature, quantum Hall effect, magnetic oscillation, etc., which are intimately connected to Landau diamagnetism and the concomitant Aharonov–Bohm phase. These attributes are characteristics of two-dimensional quantum solids such as graphene, interfaces of oxides and some topological insulators. Because these material properties hinge on the interplay of the intrinsic spin of the electron with its motion, the resultant field is known as Spintronics.

We consider a representative quantum system, namely a tight-binding chain, in which an electron can tunnel to nearest-neighbour sites with equal probability. When an AC drive is applied, a fascinating phenomenon called ‘dynamic localisation occurs – the electron keeps coming back to its starting site for specific values of amplitude and frequency of the drive. While this is a zero-temperature coherent effect, we enquire whether the oscillatory field has its influence on finite temperature, incoherent, Drude-like transport and quantum diffusive motion. Our treatment of dissipative dynamics is based on the adaptation of the well-known spin-boson model under Ohmic dissipation.