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We consider a question motivated by the third law of thermodynamics: Can there be a local temperature arbitrarily close to absolute zero in a nonequilibrium quantum system? We consider nanoscale quantum conductors with the source reservoir held at finite temperature and the drain held at or near absolute zero, a problem outside the scope of linear response theory. We obtain local temperatures close to absolute zero when electrons originating from the finite temperature reservoir undergo destructive quantum interference. The local temperature is computed by numerically solving a nonlinear system of equations describing equilibration of a scanning thermoelectric probe with the system, and we obtain excellent agreement with analytic results derived using the Sommerfeld expansion. A local entropy for a nonequilibrium quantum system is introduced and used as a metric quantifying the departure from local equilibrium. It is shown that the local entropy of the system tends to zero when the probe temperature tends to zero, consistent with the third law of thermodynamics. [ABSTRACT FROM AUTHOR]

It is shown that quantum interference can be employed to create an exciton transistor. An applied potential gates the quasiparticle motion and also discriminates between quasiparticles of differing binding energy. When implemented within nanoscale assemblies, such control elements could mediate the flow of energy and information. Quantum interference can also be used to dissociate excitons as an alternative to using heterojunctions. A finite molecular setting is employed to exhibit the underlying discrete, two-particle, mesoscopic analog to Fano antiresonance. Selected entanglement measures are shown to distinguish regimes of behavior which cannot be resolved from population dynamics alone. [ABSTRACT FROM AUTHOR]

A generalization of Büttiker's voltage probe concept for nonzero temperatures is an open third terminal of a quantum thermoelectric circuit. An explicit analytic expression for the thermoelectric correction to an ideal quantum voltage measurement in linear response is derived and interpreted in terms of local Peltier cooling/heating within the nonequilibrium system. The thermoelectric correction is found to be large (up to ±24% of the peak voltage) in a prototypical ballistic quantum conductor (graphene nanoribbon). The effects of measurement nonideality are also investigated. Our findings have important implications for precision local electrical measurements. [ABSTRACT FROM AUTHOR]

We show that a local measurement of temperature and voltage for a quantum system in steady state, arbitrarily far from equilibrium, with arbitrary interactions within the system, is unique when it exists. This is interpreted as a consequence of the second law of thermodynamics. We further derive a necessary and sufficient condition for the existence of a solution. In this regard, we find that a positive temperature solution exists whenever there is no net population inversion. However, when there is a net population inversion, we may characterize the system with a unique negative temperature. Voltage and temperature measurements are treated on an equal footing: They are simultaneously measured in a noninvasive manner, via a weakly coupled thermoelectric probe, defined by requiring vanishing charge and heat dissipation into the probe. Our results strongly suggest that a local temperature measurement without a simultaneous local voltage measurement, or vice versa, is a misleading characterization of the state of a nonequilibrium quantum electron system. These results provide a firm mathematical foundation for voltage and temperature measurements far from equilibrium. [ABSTRACT FROM AUTHOR]

A theory of local temperature measurement of an interacting quantum electron system far from equilibrium via a floating thermoelectric probe is developed. It is shown that the local temperature so defined is consistent with the zeroth, first, second, and third laws of thermodynamics, provided the probe-system coupling is weak and broadband. For non-broadband probes, the local temperature obeys the Clausius form of the second law and the third law exactly, but there are corrections to the zeroth and first laws that are higher order in the Sommerfeld expansion. The corrections to the zeroth and first laws are related, and can be interpreted in terms of the error of a nonideal temperature measurement. These results also hold for systems at negative absolute temperature. [ABSTRACT FROM AUTHOR]

We present a theoretical approach for understanding the stability of simple metal nanowires, in particular, monovalent metals such as the alkalis and noble metals. Their cross sections are of order 1 nm, so that small perturbations from external (usually thermal) noise can cause large geometrical deformations. The nanowire lifetime is defined as the time required for making a transition into a state with a different cross-sectional geometry. This can be a simple overall change in radius, or a change in the cross-section shape, or both. We develop a stochastic field theoretical model to describe this noise-induced transition process in which the initial and final states correspond to locally stable states on a potential surface derived by solving the Schrodinger equation for the electronic structure of the nanowire numerically. The numerical string method is implemented to determine the optimal transition path governing the lifetime. Using these results, we tabulate the lifetimes of sodium and gold nanowires for several different initial geometries. [ABSTRACT FROM AUTHOR]

We investigate the local electron temperature distribution in graphene nanoribbon and graphene junctions subject to an applied thermal gradient. Using a realistic model of a scanning thermal microscope, we predict quantum temperature oscillations whose wavelength is related to that of Friedel oscillations. Experimentally this wavelength can be tuned over several orders of magnitude by gating or doping, bringing quantum temperature oscillations within reach of the spatial resolution of existing measurement techniques. [ABSTRACT FROM AUTHOR]

The exact ground-state exchange-correlation functional of Kohn-Sham density functional theory yields the exact transmission through an Anderson junction at zero bias and temperature. The exact impurity charge susceptibility is used to construct the exact exchange-correlation potential. We analyze the successes and limitations of various types of approximations, including smooth and discontinuous functionals of the occupation, as well as symmetry-broken approaches. [ABSTRACT FROM AUTHOR]

Transport through an Anderson junction (two macroscopic electrodes coupled to an Anderson impurity) is dominated by a Kondo peak in the spectral function at zero temperature. We show that the single-particle Kohn-Sham potential of density-functional theory reproduces the linear transport, despite the lack of a Kondo peak in its spectral function. Using Bethe ansatz techniques, we calculate this potential for all coupling strengths, including the crossover from mean-field behavior to charge quantization caused by the derivative discontinuity. A simple and accurate interpolation formula is also given. [ABSTRACT FROM AUTHOR]

A key question in the thermodynamics of open quantum systems is how to partition thermodynamic quantities such as entropy, work, and internal energy between the system and its environment. We show that the only partition under which entropy is nonsingular is based on a partition of Hilbert space, which assigns half the system-environment coupling to the system and half to the environment. However, quantum work partitions nontrivially under Hilbert-space partition, and we derive a work sum rule that accounts for quantum work at a distance. All state functions of the system are shown to be path independent once this nonlocal quantum work is properly accounted for. Our results are illustrated with application to a driven resonant level strongly coupled to a reservoir.