Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out…
Mathematical Physics
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Quantum states are the key mathematical objects in quantum theory. It is\n therefore surprising that physicists have been unable to agree on what a\n quantum state truly represents. One possibility is that a pure quantum state\n…

Central to the EPR paradox is a 'thought experiment' in which two spins are initially coupled to a state with S = 0 and are then separated to a large distance, at which they can be separately observed. Quantum mechanics apparently predicts that the…

A spin1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by…

Two classically identical expressions for the mutual information generally differ when the systems involved are quantum. This difference defines the quantum discord. It can be used as a measure of the quantumness of correlations. Separability of the…

We present a classical protocol to efficiently simulate any purestate quantum computation that involves only a restricted amount of entanglement. More generally, we show how to classically simulate purestate quantum computations on n qubits by…

Advances in mathematics and physics have often occurred together. The development of Newton’s theory of mechanics and the simultaneous development of the techniques of calculus constitute a classic example of this phenomenon. However, as mathematics…

A state of a composite quantum system is called classically correlated if it can be approximated by convex combinations of product states, and EinsteinPodolskyRosen correlated otherwise. Any classically correlated state can be modeled by a…

An unknown quantum state ‖φ〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EinsteinPodolskyRosen (EPR) correlations. To do so the sender, ‘‘Alice,’’ and the receiver, ‘‘Bob,’’ must…

It is shown that $2+1$ dimensional quantum YangMills theory, with an action consisting purely of the ChernSimons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional…

Computational fluid dynamics (CFD) modeling of tricklebed reactors with detailed interstitial flow solvers has remained elusive mostly due to the extreme CPU and memory intensive constraints. Here, we developed a comprehensible and scalable CFD…

Addresses various problems encountered in designing a computer to exactly simulate physics. These include: simulating time; probability simulation; universal quantum simulators; probabilistic simulation of quantum systems using a classical computer;…

We observe strong violation of Bells inequality in an EinsteinPodolskyRosentype experiment with independent observers. Our experiment definitely implements the ideas behind the wellknown work by Aspect et al. We for the first time fully enforce…

Practical application of the generalized Bell’s theorem in the socalled key distribution process in cryptography is reported. The proposed scheme is based on the Bohm’s version of the EinsteinPodolskyRosen gedanken experiment and Bell’s theorem…

Nonrelativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the…

The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. It is urged that in further examination of this…

Quantum physics has remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (nondeterminism) and does not allow copying of unknown states (nocloning). Quantum correlations may be stronger than any classical…

These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in 2…

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more…

A linear map Φ from n to m is completely positive iff it admits an expression Φ(A)=ΣiViAVi where Vi are nm matrices.
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