Problems in Number Theory related to Mathematical Physics
... The total number of primes is infinite (as mentioned above) and this fact has been known since ancient times and is attributed to Euclid. The proof is quite simple and we will give the reasoning: The idea is to prove the statement by contradiction. This means that instead of trying to prove directly ...
... The total number of primes is infinite (as mentioned above) and this fact has been known since ancient times and is attributed to Euclid. The proof is quite simple and we will give the reasoning: The idea is to prove the statement by contradiction. This means that instead of trying to prove directly ...
Monte Carlo Studies of Ising Spin Glasses and Random Field Systems
... change the magnetic properties of these material and can give rise to a new sort of phase transitions. In many cases even a completely new kind of low-temperature phase, the spin glass phase, might occur, which is in some sense ordered but does not possess a translationally invariant magnetic patter ...
... change the magnetic properties of these material and can give rise to a new sort of phase transitions. In many cases even a completely new kind of low-temperature phase, the spin glass phase, might occur, which is in some sense ordered but does not possess a translationally invariant magnetic patter ...
Wigner`s Dynamical Transition State Theory in
... the potential energy surface. Certainly for one degree-of-freedom (DoF) Hamiltonian systems (i.e. one configuration space coordinate and one associated momentum) one can understand all possible dynamics from the shape of the potential energy surface. This is definitely not true for more than one DoF ...
... the potential energy surface. Certainly for one degree-of-freedom (DoF) Hamiltonian systems (i.e. one configuration space coordinate and one associated momentum) one can understand all possible dynamics from the shape of the potential energy surface. This is definitely not true for more than one DoF ...
Ph.D. thesis - Chin Lab at the University of Chicago
... trust. Cheng, I cannot thank you enough. The margin here is too narrow for writing. I thank Prof. Nathan Gemelke, who spent three years and three months working as my postdoc. I always enjoyed the numerous “small talks” when Nate entered the lab and started telling us about a new device, a novel tec ...
... trust. Cheng, I cannot thank you enough. The margin here is too narrow for writing. I thank Prof. Nathan Gemelke, who spent three years and three months working as my postdoc. I always enjoyed the numerous “small talks” when Nate entered the lab and started telling us about a new device, a novel tec ...
Quantum Databases
... were all willing to delay finalizing their daily work schedules until the evening of the previous day; high-priority events could now be added at short notice with much less disruption. The uncertainty of not knowing your schedule until the day before may be worrisome to certain employees, but in hi ...
... were all willing to delay finalizing their daily work schedules until the evening of the previous day; high-priority events could now be added at short notice with much less disruption. The uncertainty of not knowing your schedule until the day before may be worrisome to certain employees, but in hi ...
Many Body Physics
... The answer to the first question is without surprise, and can be found in all standard textbooks on solid state physics. The answer to the second question is much more surprising, since in practice the free electron theory works extremely well to describe most of the solids. When one is faced with s ...
... The answer to the first question is without surprise, and can be found in all standard textbooks on solid state physics. The answer to the second question is much more surprising, since in practice the free electron theory works extremely well to describe most of the solids. When one is faced with s ...
FRACTIONAL QUANTUM HALL STATES IN CONTINUUM AND
... In this dissertation, I will present theoretical studies on several aspects of quantum Hall states in both continuum and lattice systems. In the continuum case, one can understand the quantum Hall states starting from the Landau levels of charged particles moving in a magnetic field. If an integral ...
... In this dissertation, I will present theoretical studies on several aspects of quantum Hall states in both continuum and lattice systems. In the continuum case, one can understand the quantum Hall states starting from the Landau levels of charged particles moving in a magnetic field. If an integral ...
Disorder and entropy rate in discrete time quantum walks
... to quantify the entanglement also allows for studying the thermodynamical aspects of quantum walks [67, 68]. Similarly to transport [39–43], perfect state transfer [69] can be understood in terms of quantum walks. Decoherence in quantum walks can also lead to interesting behaviors, for a review see ...
... to quantify the entanglement also allows for studying the thermodynamical aspects of quantum walks [67, 68]. Similarly to transport [39–43], perfect state transfer [69] can be understood in terms of quantum walks. Decoherence in quantum walks can also lead to interesting behaviors, for a review see ...
Chap 15 Quantum Physics Physics
... quantum mechanics M. Planck, in 1900, found that the energy of waves could be described as consisting of small packets or quanta, A. Einstein further developed this idea to show that an EM wave could be described as a particle - the photon with a discrete quanta of energy that was dependent on its f ...
... quantum mechanics M. Planck, in 1900, found that the energy of waves could be described as consisting of small packets or quanta, A. Einstein further developed this idea to show that an EM wave could be described as a particle - the photon with a discrete quanta of energy that was dependent on its f ...
Quantum Fingerprints that Keep Secrets
... In the context of this work the meaning of (classical) fingerprints is as follows. Given a binary string x of length n, we want to efficiently produce its “partial description” by d bits, typically with d ≪ n, such that given only the description of x and any y ∈ {0, 1}n one can test, with high accu ...
... In the context of this work the meaning of (classical) fingerprints is as follows. Given a binary string x of length n, we want to efficiently produce its “partial description” by d bits, typically with d ≪ n, such that given only the description of x and any y ∈ {0, 1}n one can test, with high accu ...
Endomorphism Bialgebras of Diagrams and of Non
... construct explicit examples of such and check all the necessary properties. This gets even more complicated if we have to verify that something like a comodule algebra over a bialgebra is given. Bialgebras and comodule algebras, however, arise in a very natural way in non-commutative geometry and in ...
... construct explicit examples of such and check all the necessary properties. This gets even more complicated if we have to verify that something like a comodule algebra over a bialgebra is given. Bialgebras and comodule algebras, however, arise in a very natural way in non-commutative geometry and in ...
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: