Type-III Superconductivity.

Superconductivity remains one of most fascinating quantum phenomena existing on a macroscopic scale. Its rich phenomenology is usually described by the Ginzburg-Landau (GL) theory in terms of the order parameter, representing the macroscopic wave function of the superconducting condensate. The GL theory addresses one of the prime superconducting properties, screening of the electromagnetic field because it becomes massive within a superconductor, the famous Anderson-Higgs mechanism. Here the authors describe another widely-spread type of superconductivity where the Anderson-Higgs mechanism does not work and must be replaced by the Deser-Jackiw-Templeton topological mass generation and, correspondingly, the GL effective field theory must be replaced by an effective topological gauge theory. These superconductors are inherently inhomogeneous granular superconductors, where electronic granularity is either fundamental or emerging. It is shown that the corresponding superconducting transition is a 3D generalization of the 2D Berezinskii-Kosterlitz-Thouless vortex binding-unbinding transition. The binding-unbinding of the line-like vortices in 3D results in the Vogel-Fulcher-Tamman scaling of the resistance near the superconducting transition. The authors report experimental data fully confirming the VFT behavior of the resistance.

Landauer bound for analog computing systems.

By establishing a relation between information erasure and continuous phase transitions we generalize the Landauer bound to analog computing systems. The entropy production per degree of freedom during erasure of an analog variable (reset to standard value) is given by the logarithm of the configurational volume measured in units of its minimal quantum. As a consequence, every computation has to be carried on with a finite number of bits and infinite precision is forbidden by the fundamental laws of physics, since it would require an infinite amount of energy.

Generalized Landauer bound as a universal thermodynamic entropy in continuous phase transitions.

The classic Landauer bound can be lowered when erasure errors are permitted. Here we point out that continuous phase transitions characterized by an order parameter can also be viewed as information erasure by resetting a certain number of bits to a standard value. The information-theoretic expression for the generalized Landauer bound in terms of error probability implies thus a universal form for the thermodynamic entropy in the partially ordered phase. We explicitly show that the thermodynamic entropy as a function of interaction parameters and temperature is identical to the information-theoretic expression in terms of error probability alone in the specific example of the Hopfield neural network model of associative memory, a distributed information-processing system of many interacting stochastic bits. In this framework the Landauer bound sets a lower limit for the work associated with "remembering" rather than "forgetting."

Quantum pattern retrieval by qubit networks with Hebb interactions.

Qubit networks with long-range interactions inspired by the Hebb rule can be used as quantum associative memories. Starting from a uniform superposition, the unitary evolution generated by these interactions drives the network through a quantum phase transition at a critical computation time, after which ferromagnetic order guarantees that a measurement retrieves the stored pattern. The maximum memory capacity of these qubit networks is reached at a memory density alpha=p/n=1.