ESI Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
... Z the normalization factor (partition function) and β = 1/T the inverse temperature. Units are chosen so that Boltzmann’s constant equals 1. The thermal expectation value of some observable O will be denoted by hOi = Z −1 Tr O exp(−βH). In the proof of BEC we focus on dimensions d ≥ 3, but, using th ...
... Z the normalization factor (partition function) and β = 1/T the inverse temperature. Units are chosen so that Boltzmann’s constant equals 1. The thermal expectation value of some observable O will be denoted by hOi = Z −1 Tr O exp(−βH). In the proof of BEC we focus on dimensions d ≥ 3, but, using th ...
Physical Chemistry
... quantum state, to order lsI2it can only change to the n f 1 states. Again, as lsI2 increases, more molecules change their states by a single quantum, but a large vibrational excitation of a single molecule is never attained as long as ls12 << 1. In summary, coherent Raman experiments using femtoseco ...
... quantum state, to order lsI2it can only change to the n f 1 states. Again, as lsI2 increases, more molecules change their states by a single quantum, but a large vibrational excitation of a single molecule is never attained as long as ls12 << 1. In summary, coherent Raman experiments using femtoseco ...
Quantum Computing and Quantum Topology
... If a physical system were to have quantum topological (necessarily nonlocal) degrees of freedom, which were insensitive to local probes, then information contained in them would be automatically protected against errors caused by local interactions with the ...
... If a physical system were to have quantum topological (necessarily nonlocal) degrees of freedom, which were insensitive to local probes, then information contained in them would be automatically protected against errors caused by local interactions with the ...
ppt1 - Zettaflops
... • A Quantum computer can probably be built eventually, but not right away. Maybe in 20 years. We don’t know yet what it will look like. • It would exponentially speed up a few computations like factoring, thereby breaking currently used digital signatures and public key cryptograp (Shor algorithm) • ...
... • A Quantum computer can probably be built eventually, but not right away. Maybe in 20 years. We don’t know yet what it will look like. • It would exponentially speed up a few computations like factoring, thereby breaking currently used digital signatures and public key cryptograp (Shor algorithm) • ...
Document
... I. Theorems that stem from the following general assumptions about the character of the macroscopic motion a r e of great importance in statistical thermodynamics: 1) the microscopic motion obeys the laws of mechanics and is, therefore, reversible in time; 2) a system in thermodynamic equilibrium wi ...
... I. Theorems that stem from the following general assumptions about the character of the macroscopic motion a r e of great importance in statistical thermodynamics: 1) the microscopic motion obeys the laws of mechanics and is, therefore, reversible in time; 2) a system in thermodynamic equilibrium wi ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.