Scientific Series

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)

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 .

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.

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.

The minimal dimension of the Hilbert space that hosts states of an entangled pair of photons can be extremely high. The process of spontaneous parametric down-conversion (SPDC) is a possible way of producing highly entangled photon pairs, in both the spatial and temporal parts of the wave function. However, the most common approximations that are used in the analytical treatment of SPDC hinder the possibility of noticing further structures of the single joint modes. We used a more general formalism, showing that the entangled modes are still eigenfunctions of the orbital angular momentum, but the radial modes are far from the usual ones and they show novel interesting features that might be explained by introducing an additional quantum number. The problem of dealing with SPDC states has two faces: we need to know with enough confidence what state are created, and we need to know with enough confidence what states we are projecting on, upon measurement. We tried to approach both these problems together, and we showed that high dimensional entanglement shields the amount of information that can be stored in a photon from imperfect measurements. In my talk I will present both these aspects of high-dimensionally entangled states of photon pairs.

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.

The distinction between a realist interpretation of quantum theory that is psi-ontic and one that is psi-epistemic is whether or not a difference in the quantum state necessarily implies a difference in the underlying ontic state. Psi-ontologists believe that it does, psi-epistemicists that it does not. This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program. I will review the evidence in favour of the psi-epistemic approach and describe the pre-existing reasons for thinking that if a quantum state represents knowledge about reality then it is not reality as we know it, i.e., it is not the kind of reality that is posited in the standard hidden variable framework. I will argue that the PBR theorem provides additional clues for "what has to give" in the hidden variable framework rather than providing a reason to retreat from the psi-epistemic position. The first assumption of the theorem - that holistic properties may exist for composite systems, but do not arise for unentangled quantum states - is only appealing if one is already predisposed to a psi-ontic view. The more natural assumption of separability (no holistic properties) coupled with the other assumptions of the theorem rules out both psi-ontic and psi-epistemic models and so does not decide between them. The connection between the PBR theorem and other no-go results will be discussed. In particular, I will point out how the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory, regardless of the status of separability (though not in the form posited by PBR). I will also consider the connection of PBR to the failure of local causality by considering an experimental scenario which is in a sense a time-inversion of the PBR scenario.

It is well known that on-shell recursion relation can be applied to tree-level amplitude in string theory. One technical issue of the application is the sum of infinite middle on-shell states. We discuss how we can do the sum exactly to reproduce the known result.

With the emergence of the dark sector in cosmology,  a variety of modified theories of gravity have come to the fore. I will discuss a framework which can be used to test gravity on large scales and the observational programmes that might lead to the tightest constraints.