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Shadows of the Mind: A Search for the Missing Science of Consciousness
TLDR
Penrose presents a version of the theorem in which the true but unprovable sentence is an assertion that a certain computer program runs on forever.
Large fluctution for a non linear heat equation with noise
Studies a nonlinear heat equation in a finite interval of space subject to a white noise forcing term. The equation without the forcing term exhibits several equilibrium configurations, two of which…
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Philosophy of Mathematics : An Introduction to the World of Proofs and Pictures
This example indicates that there is more than one way to look at the role of pictures in proof. The weakest claim is that a picture can serve as an aid to inspire a proof. The mathematician…
Commutators and self-adjointness of Hamiltonian operators
A time dependent approach to self-adjointness is presented and it is applied to quantum mechanical Hamiltonians which are not semi-bounded. Sufficient conditions are given for self-adjointness of…
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Inequalities and uncertainty principles
Sobolev inequalities give lower bounds for quantum mechanical Hamiltonians. These inequalities are derived from commutator inequalities related to the Heisenberg uncertainty principle.
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Invariant cones and uniqueness of the ground state for fermion systems
A perturbation theory is developed for self‐adjoint operators whose resolvents leave a cone invariant. The Perron‐Frobenius theory may be applied to the perturbed operator to conclude that its lowest…
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Weak Lebesgue spaces and quantum mechanical binding
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Review: Michael Reed and Barry Simon, Methods of modern mathematical physics, vol. III, Scattering theory, and Michael Reed and Barry Simon, Methods of modern mathematical physics, vol. IV, Analysis…
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Diffusion, quantum theory, and radically elementary mathematics
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also…
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Self-Adjoint Operators
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