Cold Atoms For Testing Quantum Mechanics and Parity Violation In Gravitation

Techniques of Atom trapping and laser cooling have proved to be very important tools in probing many aspects of fundamental physics. In this talk I wish to present ideas on how they may used to settle certain issues in the foundational aspects of quantum mechanics on the one hand and about some quantum gravitational interactions of matter that violate parity and time-reversal, on the other hand.Comment: Revtex, 8 page

Three Lectures on Chiral Symmetry

In these lectures I cover various aspects of Chiral Symmetry in the hadronic world from a pre-QCD perspective. I also discuss the absence of spontaneous symmetry breaking in d=4 large N O(N) models.Comment: 23 pages, 9 figure

All Conformal Effective String Theories are Isospectral to Nambu-Goto Theory

It is shown that all Polchinski-Strominger effective string theories are \emph{isospectral} to Nambu-Goto theory. The relevance of these results to QCD-Strings is discussed.Comment: 4 pages in REVTEX. Various typos fixed, the abstract and discussions modestly enlarged and presentation improved in v

Does the first part of the second law also imply its second part?

Sommerfeld called the first part of the second law to be the entropy axiom, which is about the existence of the state function entropy. It was usually thought that the second part of the second law, which is about the non-decreasing nature of entropy of thermally isolated systems, did not follow from the first part. In this note, we point out the surprise that the first part in fact implies the second part.Comment: 7 pages, 4 figures, prepared in JHEP styl

Are weak measurements really necessary for Leggett-Garg type measurements?

Leggett-Garg inequalities are an important milestone in our quest to bridge the classical-quantum divide. An experimental investigation of these inequalities requires the so called \emph{non-invasive measurements}(NIM). It has become popular to invoke weak measurements as the means of realising NIMs to very good approximation, because of their allegedly low disturbance of systems under measurement. In this note, this is shown to be a myth; it is shown, by simple estimates of errors, that for comparable levels of statistical errors, even the strong or projective measurements can be used. In fact, it is shown that resource-wise, strong measurements are even preferable.Comment: 5 pages in Revte

Unknown single oscillator coherent states do have statistical significance

It is shown, contrary to popular belief, that {\it single unknown} oscillator coherent states can be endowed with a {\em measurable statistical significance}.Comment: 4 pages in Revte

On repeated (continuous) weak measurements of a single copy of an unknown quantum state

In this paper we investigate repeated weak measurements,without post-selection, on a \emph{single copy} of an \emph{unknown} quantum state. The resulting random walk in state space is precisely characterised in terms of joint probabilities for outcomes. We conclusively answer, in the negative, the very important question whether the statistics of such repeated measurements can determine the unknown state. We quantify the notion of error in this context as the departure of a suitably averaged density matrix from the initial state. When the number of weak measurements is small the original state is preserved to a great degree, but only an ensemble of such measurements, of a complete set of observables, can determine the unknown state. By a careful analysis of errors, it is shown that there is a precise tradeoff between errors and \emph{invasiveness}. Lower the errors, greater the invasiveness. Though the outcomes are not independently distributed, an analytical expression is obtained for how averages are distributed, which is shown to be the way outcomes are distributed in a \emph{strong measurement}. An \emph{error-disturbance} relation, though not of the Ozawa-type, is also derived. In the limit of vanishing errors, the invasiveness approaches what would obtain from strong measurements.Comment: 5 pages in RevTeX 4; in this latest version, the title has been modified a bit, abstract cleaned up and a note added about a work by Tamir, Cohen and Priel that appeared subsequent to my work addressing related issue

A critique of Sadi Carnot's work and a mathematical theory of the caloric

In this work, Sadi Carnot;s fundamental work is critically examined, and contrasted with modern thermodynamics. A mathematical theory of his work is given on the basis of the observation that in caloric theory dQ is a perfect differential.Comment: 17 pages, 8 figures, prepared in JHEP styl

On Finite Size Effects in d=2d=2 Quantum Gravity

A systematic investigation is given of finite size effects in $d=2$ quantum gravity or equivalently the theory of dynamically triangulated random surfaces. For Ising models coupled to random surfaces, finite size effects are studied on the one hand by numerical generation of the partition function to arbitrary accuracy by a deterministic calculus, and on the other hand by an analytic theory based on the singularity analysis of the explicit parametric form of the free energy of the corresponding matrix model. Both these reveal that the form of the finite size corrections, not surprisingly, depend on the string susceptibility. For the general case where the parametric form of the matrix model free energy is not explicitly known, it is shown how to perform the singularity analysis. All these considerations also apply to other observables like susceptibility etc. In the case of the Ising model it is shown that the standard Fisher-scaling laws are reproduced.Comment: 9 pages, Late

Three results on weak measurements

Three recent results on weak measurements are presented. They are: i) repeated measurements on a single copy can not provide any information on it and further, that in the limit of very large such measurements, weak measurements have exactly the same characterstics as strong measurements, ii) the apparent non-invasiveness of weak measurements is \emph{illusory} and they are no more advantageous than strong measurements even in the specific context of establishing Leggett-Garg inequalities, when errors are properly taken into account, and, finally, iii) weak value measurements are optimal, in the precise sense of Wootters and Fields, when the post-selected states are mutually unbiased with respect to the eigenstates of the observable whose weak values are being measured. Notion of weak value coordinates for state spaces are introduced and elaborated.Comment: 7 pages in Revtex, 2 figures, to appear in {\it Quantum Measurements} , Current Scienc