Scientific Series

Five decades ago, Aharonov and Bohm illustrated the indispensable role of the vector potential in quantum dynamics by showing (theoretically) that scattering electrons around a solenoid, no matter how thin, would give rise to a non-trivial cross section that had a periodic dependence on the product of charge and total magnetic flux. (This periodic dependence is due to the topological nature of the interaction.) We extend the Aharonov-Bohm analysis to the field theoretic domain: starting with the quantum vacuum (with zero particles) we compute explicitly the rate of production of electrically charged particle-antiparticle pairs induced by shaking a solenoid at some fixed frequency. (This body of work can be found in arXiv: 0911.0682 and 1003.0674.) Part II: The N-Body Problem in General Relativity from Perturbative QFT In the second portion of the talk, I will describe how one may use methods usually associated with perturbative quantum field theory to develop what is commonly known as the post-Newtonian program in General Relativity -- the weak field, non-relativistic, gravitational dynamics of compact astrophysical objects. The 2 body aspect of the problem is a large industry by now, driven by the need to model the gravitational waves expected from compact astrophysical binaries. I will discuss my efforts to generalize these calculations to the N-body case. (This work can be found in arXiv: 0812.0012.)

In this talk I will discuss the applications of the gauge/gravity duality to the strongly coupled quark gluon plasma, focusing in particular on the role of the shear viscosity to entropy ratio. It has been argued that the lower bound on the shear viscosity to entropy density in strongly coupled plasmas can be understood in terms of microcausality violation in the dual gravitational description. However, since the transport properties of the system characterize its infrared dynamics, while the causality of the theory is determined by its ultraviolet behavior, the link between the viscosity bound and microcausality should not be applicable in theories that undergo low temperature phase transitions. I will discuss an explicit holographic model confirming this fact, in which there is a ``decoupling'' of UV from IR physics.

The counter-intuitive phenomena in quantum mechanics are often based on the counter-factual (or virtual) processes. The famous example is the Hardy paradox, which has been recently solved in two independent experiments. Also, the delayed choice experiment and one of quantum descriptions of the closed time like curves can be also examples of the counter-intuitive phenomena. The counter-factual processes can be characterized by the weak value initiated by Yakir Aharonov and his colleagues. In this talk, I will introduce the weak value from the probability theory and the connection to the counter-factual processes in these examples.

AdS/CFT has proven itself a powerful tool in extending our understanding of strongly coupled quantum theories. While studies of AdS/CFT have predominantly focused on tree level calculations, there has been growing interest in the loop effect recently. We studied the 1-loop correction to the gauge boundary-to-boundary correlator due to its coupling to a complex scalar field. In this talk, I would outline our main results, explain the Cutkosky rule in AdS space, and discuss an extra divergence we found in both real and imaginary part of the loop integral. I would then combine our analysis with the replica trick to demonstrate a possible application where one attempts to calculate the DC conductivity in a condensed matter system with random disorder and discuss the limitation and difficulties of our method in its current form.

I'll describe a connection between uncertainty relations, information locking and low-distortion embeddings of L2 into L1. Exploiting this connection leads to the first explicit construction of entropic uncertainty relations for a number of measurements that is polylogarithmic in the dimension d while achieving an average measurement entropy of (1-e) log d for arbitrarily small e. From there, it is straightforward to obtain the first strong information locking scheme that is efficiently computable using a quantum computer. This locking scheme can be interpreted as a method for encrypting classical messages using a key of size much smaller than the message length. Other applications include efficient encodings for amortized quantum identification over classical channels and new string commitment protocols.

The average quantum physicist on the street believes that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian $H=p^2+ix^3$, which is obviously not Dirac Hermitian, has a real positive discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While $H=p^2+ix^3$ is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined space reflection P and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. Some of these properties have recently been verified in laboratory experiments. If one generalizes classical mechanics into the complex domain, the resulting theories have equally remarkable properties.

The second law of thermodynamics tells that physics imposes a fundamental constraint on the efficiency of all thermal machines. Here I will address the question of whether size imposes further constraints upon thermal machines, namely whether there is a minimum size below which no machine can run, and whether when they are small if they can still be efficient? I will present a simple model which shows that there is no size limitation and no limit on the efficiency of thermal machine and that this leads to a unified view of small refrigerators, pumps and engines.

We discuss the coupling of fermions to holographic superconductors in 3+1 and 4+1 (bulk) dimensions. We do so from a top-down perspective, by considering the reduction of the fermionic sector in recently found consistent truncations of type IIB and D=11 supergravity on squashed Sasaki-Einstein manifolds, which notably retain a finite number of charged (massive) modes. The truncations in question also include the string/M-theory embeddings of various models which have been proposed to describe systems with non-relativistic scale invariance via holography. We show that the lower-dimensional effective action for the fermion modes includes certain interactions that had been discussed in bottom-up constructions, as well as a variety of new couplings that may be relevant for applications of holographic techniques to the study of condensed matter systems

The idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT is developed. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, I consider the anomalous dimensions, gamma(n,l), of the double-trace operators of the form O (del^2)^n (del)^l O. Purely from the CFT, perturbative unitarity places a bound on these dimensions; non-renormalizable AdS interactions lead to violations of the bound at large values of n. I also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. The presence of the heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonance-like behavior in gamma(n,l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, I demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d+1 dimensions

Entanglement renormalization is a coarse-graining transformation for quantum lattice systems. It produces the multi-scale entanglement renormalization ansatz, a tensor network state used to represent ground states of strongly correlated systems in one and two spatial dimensions. In 1D, the MERA is known to reproduce the logarithmic violation of the boundary law for entanglement entropy, S(L)~log L, characteristic of critical ground states. In contrast, in 2D the MERA strictly obeys the entropic boundary law, S(L)~L, characteristic of gapped systems and a class of critical systems. Therefore a number of highly entangled 2D systems, such as free fermions with a 1D Fermi surface, Fermi liquids and spin Bose metals, which display a logarithmic violation of the boundary law, S(L)~L log L, cannot be described by a regular 2D MERA. It is well-known that at low energies, a many-body system may decouple into two or more independent degrees of freedom (e.g. spin-charge separation in 1D systems of electrons). In this talk I will explain how, in systems where low energy decoupling occurs, entanglement renormalization can be used to obtain an explicit decoupled description. The resulting tensor network state, the branching MERA, can reproduce a logarithmic violation of the boundary law in 2D and, as additional numeric evidence also suggests, might be a good ansatz for the highly entangled systems with a 1D Fermi (or Bose) surface mentioned above. In addition, after recalling that the MERA can be regarded as a specific (discrete) realization of the holographic principle, we will see that the branching MERA leads to exotic holographic geometries.

CRESST is a cryogenic dark matter search located at the Laboratori Nazionali del Gran Sasso in Italy. Scintillating CaWO4 crystals are operated as cryogenic calorimeters. The phonon (heat) signal measured with a tungten transition edge sensor on the surface of these crystals allows a precise determination of the energy deposited in the crystal, independent of the type of interaction. A light signal, simultaneously registered by a separate cryogenic detector, serves to identify the type of interaction. This phonon/light technique allows a discrimination of electron recoils induced by radioative backgrounds from the searched nuclear recoils with high efficiency ,and, to some extent, even to determine which type of nucleus was recoiling. I will present results from 564 kg-days of data of the presently still ongoing run, which reveal an unexpected excess of oxygen recoils. To shine some light on the nature of these events, I will discuss possible backgrounds in some detail.