Theoretical Chemistry I Quantum Mechanics
... Although the time-dependent and the time-independent Schrödinger equations look rather simple, their solution is often not trivial. They correspond to second-order partial differential equations. Here we will consider some simple problems. For the sake of simplicity, we consider piecewise continuou ...
... Although the time-dependent and the time-independent Schrödinger equations look rather simple, their solution is often not trivial. They correspond to second-order partial differential equations. Here we will consider some simple problems. For the sake of simplicity, we consider piecewise continuou ...
Quantum critical temperature of a modulated oscillator Lingzhen Guo, Vittorio Peano, M. Marthaler,
... increases with n − m. Our method is fairly general and it shows how one can go beyond the conventional large-deviation theory when the perturbation is singular. For concreteness, we analyze the distribution about the small-amplitude SVS, i.e., about the local maximum of g(Q,P ) in Fig. 1, which is o ...
... increases with n − m. Our method is fairly general and it shows how one can go beyond the conventional large-deviation theory when the perturbation is singular. For concreteness, we analyze the distribution about the small-amplitude SVS, i.e., about the local maximum of g(Q,P ) in Fig. 1, which is o ...
Three Myths about Time Reversal in Quantum Theory
... conjugation; they have fostered the third in arguing that it does not necessarily transform momentum and spin.3 However, these perspectives aside, I hope that the dissolution of these myths and the account of time reversal that I propose may be of independent interest. In place of the myths, I will ...
... conjugation; they have fostered the third in arguing that it does not necessarily transform momentum and spin.3 However, these perspectives aside, I hope that the dissolution of these myths and the account of time reversal that I propose may be of independent interest. In place of the myths, I will ...
Exponential Decay of Quantum Wave Functions
... We turn finally to L2 bounds. Combes–Thomas [15] notes that ea|x| ψ ∈ L2 , if and only if for any unit vector, ê, ψz ≡ exp(izê · x)ψ(x) has an analytic continuation from z ∈ R to {z | |Imz| < a}. Similarly if f is a non-negative function and U (s) is the unitary operator of multiplications by eisf ...
... We turn finally to L2 bounds. Combes–Thomas [15] notes that ea|x| ψ ∈ L2 , if and only if for any unit vector, ê, ψz ≡ exp(izê · x)ψ(x) has an analytic continuation from z ∈ R to {z | |Imz| < a}. Similarly if f is a non-negative function and U (s) is the unitary operator of multiplications by eisf ...
Midgap states of a two-dimensional antiferromagnetic Mott
... square of the lattice to be minus one using a spin-independent gauge in which T ij = −1 for one link of each plaquette, but T ij = +1 for the remaining three links (see fig. 1 a)). In this spin-independent gauge αx = −γz ⊗ τx ⊗ I and αy = γx ⊗ τx ⊗ I contain the identity matrix in spin-space and β = ...
... square of the lattice to be minus one using a spin-independent gauge in which T ij = −1 for one link of each plaquette, but T ij = +1 for the remaining three links (see fig. 1 a)). In this spin-independent gauge αx = −γz ⊗ τx ⊗ I and αy = γx ⊗ τx ⊗ I contain the identity matrix in spin-space and β = ...
Derivation of new quantum hydrodynamic equations using entropy
... In fact, we only assume that its kernel consists of the quantum thermal equilibrium distribution (defined in section 2) and that the operator preserves certain moments. The macroscopic variables are defined as the moments of the Wigner function over momentum space; more precisely, we consider the pa ...
... In fact, we only assume that its kernel consists of the quantum thermal equilibrium distribution (defined in section 2) and that the operator preserves certain moments. The macroscopic variables are defined as the moments of the Wigner function over momentum space; more precisely, we consider the pa ...
E.T.WHITTAKER`S QUANTUM FORMALISM
... and Schwinger, so had written an account of Whittaker’s work into my research notes of the period. In the spring of I revisited the subject, and wrote the material which can be found on pages 68–83 in Chapter 3 of my quantum mechanics (/). Here I do much the same thing (if—I hope—from a s ...
... and Schwinger, so had written an account of Whittaker’s work into my research notes of the period. In the spring of I revisited the subject, and wrote the material which can be found on pages 68–83 in Chapter 3 of my quantum mechanics (/). Here I do much the same thing (if—I hope—from a s ...
POLYNOMIAL-TIME ALGORITHMS FOR PRIME FACTORIZATION
... device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and nding discrete logarithms, two pro ...
... device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and nding discrete logarithms, two pro ...
Why Philosophers Should Care About - Philsci
... zero-knowledge proofs), and the theoretical foundations of machine learning and quantum computation. To people who work on these topics, the work of Gödel and Turing may look in retrospect like just a warmup to the “big” questions about computation. Because of this, I find it surprising that compl ...
... zero-knowledge proofs), and the theoretical foundations of machine learning and quantum computation. To people who work on these topics, the work of Gödel and Turing may look in retrospect like just a warmup to the “big” questions about computation. Because of this, I find it surprising that compl ...
Griffiths-McCoy singularities in the random transverse-field Ising spin chain Ferenc Iglo´i
... where var@ x # denotes the variance and at the critical point d 50. The Hamiltonian in Eq. ~1.2! is closely related to the transfer matrix of a classical two-dimensional layered Ising model, which was first introduced and partially solved by McCoy and Wu.8 Later the critical properties of the quantu ...
... where var@ x # denotes the variance and at the critical point d 50. The Hamiltonian in Eq. ~1.2! is closely related to the transfer matrix of a classical two-dimensional layered Ising model, which was first introduced and partially solved by McCoy and Wu.8 Later the critical properties of the quantu ...
Machine invention of quantum computing circuits by means
... here is PushGP (Spector, 2001, 2004; Spector & Robinson, 2002; Spector et al., 2005). PushGP differs from most other genetic programming systems in that it uses the Push programming language as the formalism within which evolving programs are expressed. Most other systems, by contrast, use Lisp-like ...
... here is PushGP (Spector, 2001, 2004; Spector & Robinson, 2002; Spector et al., 2005). PushGP differs from most other genetic programming systems in that it uses the Push programming language as the formalism within which evolving programs are expressed. Most other systems, by contrast, use Lisp-like ...
Bell's theorem
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Bell's theorem is a ‘no-go theorem’ that draws an important distinction between quantum mechanics (QM) and the world as described by classical mechanics. This theorem is named after John Stewart Bell.In its simplest form, Bell's theorem states:Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from ""indifference"" to ""wild extravagance"". Lawrence Berkeley particle physicist Henry Stapp declared: ""Bell's theorem is the most profound discovery of science.""Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables). Bell concluded:Bell summarized one of the least popular ways to address the theorem, superdeterminism, in a 1985 BBC Radio interview: