Scientific Series

In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation £ of possible causation: for p, q Î C,   p £ q means that q is in p’s future light cone. Fotini Markopoulou has proposed that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, in essence, by the topos Set C of presheaves on Cop.  In this talk I am going to show how Set  C may be effectively replaced by a certain model V(H) of intuitionistic set theory—frame-valued set theory—with (I hope) illuminating results. In particular, Markopoulou’s idea of viewing the universe “from the inside” will amount to placing oneself “inside” V(H). I will also sketch the role played in this framework by covering schemes and sheaves.

A local renormalization group procedure is proposed where length scale is changed in spacetime dependent manner. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical sources for low energy modes at each scale, we provide a prescription to derive background independent holographic duals for field theories. From a first principle construction, it is shown that the holographic theory dual to a D-dimensional matrix field theory is a (D+1)-dimensional quantum theory of gravity coupled with matter fields of various spins.The (D+1)-dimensional diffeomorphism invariance is a consequence of the freedom to choose different local RG schemes.

A beautiful understanding of the smallness of the neutrino masses may be obtained via the seesaw mechanism, whereby one takes advantage of the key qualitative distinction between the neutrinos and the other fermions: right-handed neutrinos are gauge singlets, and may therefore have large Majorana masses. The standard seesaw mechanism, however, does not address the apparent lack of hierarchy in the neutrino masses compared to the quarks and charged leptons, nor the large leptonic mixing angles compared to the small angles of the CKM matrix. In this talk, I will show that the singlet nature of the right-handed neutrinos may be taken advantage of in one further way in order to solve these remaining problems: Unlike particles with gauge interactions, whose numbers are constrained by anomaly cancellation, the number of gauge singlet particles is essentially undetermined. If large numbers of gauge singlet fermions are present at high energies - as is suggested, for example, by various string constructions - then the effective low energy neutrino mass matrix may be determined as a sum over many distinct Yukawa couplings, with the largest ones being the most important. This can reduce hierarchy, and lead to large mixing angles. Assuming a statistical distribution of fundamental parameters, we will show that this scenario leads to a good fit to low energy phenomenology, with only a few qualitative assumptions guided by the known quark and lepton masses. The scenario leads to predictions of a normal hierarchy for the neutrino masses, and a value for the |m_ee| mass matrix element of about 1-6 meV.

How did inflation actually happen? Precision measurements of statistical properties of primordial fluctuations generated during inflation offer a direct probe of the physics of inflation. When we calculate statistical properties of primordial fluctuations generated during inflation, we usually assume that the initial state of quantum fluctuations is in a preferred vacuum state called Bunch-Davies vacuum. While there is some motivation for choosing such a state, this is an assumption, and thus needs to be tested by observations. In this talk I will present new probes of initial state of quantum fluctuations during inflation: the 3-point function of the cosmic microwave background anisotropy, the 2-point function of galaxies, and a spectral distortion of the thermal spectrum of the cosmic microwave background.   

Electrons in conjugated organic polymers and molecules are strongly correlated since most of these systems are quasi one-dimensional.  Experimental evidences include existence of two photons below one photon state, observation of negative spin densities in polyene radicals and qualitatively different behavior of  optical gaps in polyenes and closely related symmetric cynanine dyes in the thermodynamic limiy. In this talk, I will introduce the model Hamiltonians for the electron states in conjugated systems. The DMRG method is ideally suited for their study.  Modifications to the DMRG method to obtain important low-lying states of  the systems and methods of obtaining linear and nonlinear optical response coefficients using the DMRG technique will be discussed [1-4]. Application of the method to the study of a wide variety of conjugated systems will be touched upon [5,7]. I will also discuss some recent applications of wave-packet dynamics in the study of some time-dependent phenomena [8]. References [1] S. Ramasesha, Swapan K Pati, H.R. Krishnamurthy, Z. Shuai and J. L. Br´edas, (1996) “Symmetrized DMRG method for the excited states of Hubbard models”, Phys. Rev. B 54, 7598. [2] Z. Shuai, J. L. Br´edas, Swapan K. Pati and S. Ramasesha, (1998) “Comment on the exciton binding energy in the strong correlation limit of conjugated chains”, Phys. Rev. B 58, 15329. [3] Z. Shuai, J. L. Br´edas, Swapan K. Pati and S. Ramasesha, (1997) “Quan­tum confinement effects on the ordering of the lowest-lying excited states in conjugated chains”, Phys. Rev. B 56, 9298. [4] Swapan K Pati, S. Ramasesha, Z. Shuai and J. L. Br´edas, (1999) “Dynamic nonlinear optical properties from the symmetrized density matrix renormal­ization group method”, Phys. Rev. B 59, 14827. [5] C. Raghu, Y. Anusooya Pati and S. Ramasesha, (2002) “A density matrix renormalization group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model”, Phys. Rev. B 66, 035116. [6] S. Mukhopadhyay  and  S. Ramasesha (2009) “Study of linear and nonlinear optical properties of  dendrimers using density matrix renormalization group method”,  J. Chem.  Phys.  131, 074111. [7] M. Kumar and S. Ramasesha, (2010) “A DMRG Study of the Low-Lying States of Transverse Substituted Trans-polyacetylene and Trans-polyacetylene”, Phys. Rev. B. 81, 035115 [8] Tirthankar Dutta and S. Ramasesha, (2010) “Double time window targeting technique: Real-time DMRG dynamics in Pariser-Parr-Pople model”, Phys. Rev. B 82, 035115. [9] Simil Thomas, Daniel Garcia, Karen Hallberg and S. Ramasesha "Fused Azulenes: Possible Organic Multiferroics", Phys. Rev. B RC (communicated)

When two independent analog signals, $X$ and $Y$ are added together giving $Z=X+Y$, the entropy of $Z$, $H(Z)$, is not a simple function of the entropies $H(X)$ and $H(Y)$, but rather depends on the details of $X$ and $Y$'s distributions.  Nevertheless, the entropy power inequality (EPI), which states that $e^{2H(Z)} \geq e^{2H(X)} + e^{2H(Y)}$, gives a very tight restriction on the entropy of $Z$. This inequality has found many applications in information theory and statistics.  The quantum analogue of adding two random variables is the combination of two independent bosonic modes at a beam splitter. The purpose of this talk is to give an outline of the proof of two separate generalizations of the entropy power inequality to the quantum regime.  These inequalities provide strong new upper bounds for the classical capacity of quantum additive noise channels, including quantum analogues of the additive white Gaussian noise channels.   Our proofs are similar in spirit to standard classical proofs of the EPI, but some new quantities and ideas are needed in the quantum setting. Specifically, we find a new quantum de Bruijin identity relating entropy production under diffusion to a divergence-based quantum Fisher information. Furthermore, this Fisher information exhibits certain convexity properties in the context of beam splitters.   This is joint work with Graeme Smith.

Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a conventional perturbation analysis. After a brief review of both the scalar field story and the affine quantum gravity program, examination of the procedures used in the latter surprisingly shows an analogous formulation which already implies that affine quantum gravity is not plagued by divergences that arise in a standard perturbation study. Additionally, guided by the projection operator method to deal with quantum constraints, trial reproducing kernels are introduced that satisfy the diffeomorphism constraints. Furthermore, it is argued that the trial reproducing kernels for the diffeomorphism constraints also satisfy the Hamiltonian constraint as well. 
This talk is based on arXiv:1203.0691 .

In this talk I provide a model where the late time acceleration of the universe emerges from a BCS-like condensation of sterile neutrinos. This scenario can be naturally accommodated by general relativity covariantly coupled to sterile neutrinos, where the neutrinos act like an "aether" field.  We show that when active neutrinos couple to the neutrino condensate, they oscillate at a rate proportional to the dark energy density.  As a result, the oscillation of neutrinos and dark energy are tied in with the same mechanism.  I also show that neutrinos could oscillate even if dark energy is not a neutrino condensate.  I end with a discussion of stability of this model and predictions of CPT violating oscillations of such models.

We propose a new method of unifying gravity and the Yang-Mills fields by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a constrained Spin(4) ~SO(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the Spin(4) symmetry, providing a way to couple Yang-Mills fields to spin-foams. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes  between particle states. We conclude with speculations about extension of the model to 4D and  incorporate a newly developed model of Dark Energy.

Large quantum fluctuations in certain quantum spin systems destroy long range magnetic order such as antiferromagnetism. Resulting paramagnetic states are called a quantum spin liquids. These states support emergent gauge fields [1]. Under certain conditions, emergent gauge fields condense in the ground state, leading to a chiral spin liquid state [2]. A condensed `magnetic field' for example, correspond to presence of spontaneous circulating spin current or spin `chirality'[3]. In the light of recent search for spin liquids in frustrated quantum antiferromagnets, we revive our earlier approach and show that a variety of chiral spin liquid states are possible in 2D lattices.   [1] G. Baskaran and P.W. Anderson, Phys. Rev., B 37, 580 (1988) [2] V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett., 59, 2095 (1987) [3] X.-G. Wen, F. Wilczek and A. Zee, Phys. Rev., B 39, 11413 (1989) [4] G Baskaran, Phys. Rev. Lett., 63, 2524 (1989)

Shape Dynamics first arose as a theory of particle interactions formulated without any of Newton's absolute structures. Its fundamental arena is shape space, which is obtained by quotienting Newton's kinematic framework with respect to translations, rotations and dilatations. This leads to a universe defined purely intrinsically in relational terms. It is then postulated that a dynamical history is determined by the specification in shape space of an initial shape and an associated rate of change of shape. There is a very natural way to create a theory that meets such a requirement. It fully implements Mach's principle and shows how time and local inertial frames are determined by the universe as whole. If the same principles are applied to a spatially closed universe in which geometry is dynamical, they lead rather surprisingly to a theory that, modulo some caveats, is dynamically equivalent to general relativity but dual to it in that refoliation invariance is traded for three-dimensional conformal invariance. This shows that there is a hidden three-dimensional conformal symmetry within general relativity. It is in fact what underlies York's crucial method of solution of the initial-value problem in general relativity. It is also remarkable that, as in York's work, shape dynamics inescapably introduces a mathematically distinguished notion of absolute simultaneity, the desirability of which has been found in two currently popular approaches to quantum gravity: causal dynamical triangulations and Horava gravity. I aim to express the key ideas and techniques of shape dynamics as simply as possible.