The strange equation of quantum gravity
... in various ways in the context of the theory. For instance, in AdS/CFT setting, a constant radial coordinate surface can be seen as playing the role of the ADM constant time surface, the quantisation of the corresponding constraint of the bulk gravity theory gives a WdW equation and its Hamilton-Jac ...
... in various ways in the context of the theory. For instance, in AdS/CFT setting, a constant radial coordinate surface can be seen as playing the role of the ADM constant time surface, the quantisation of the corresponding constraint of the bulk gravity theory gives a WdW equation and its Hamilton-Jac ...
Simulating a simple Quantum Computer
... eigenstate of the memory register at the times when the cursor is observed • For compactness of notation we label the eigenstates of the (in this case 4-bit) memory register, |i>, in base 10 notation. For example, |5> corresponds to the eigenstate of the memory register that is really |0101> and |15 ...
... eigenstate of the memory register at the times when the cursor is observed • For compactness of notation we label the eigenstates of the (in this case 4-bit) memory register, |i>, in base 10 notation. For example, |5> corresponds to the eigenstate of the memory register that is really |0101> and |15 ...
Hamiltonian Systems with Three or More
... the Baggot Hamiltonian, as β12 < 0 and λ > 0 the 1:1 resonance width actually decreases as the actions I1 , I2 get larger. Note also that we do not explicitly consider secondary resonances since we are interested only in the large-scale structure of the classical phase space (i.e., intersection of t ...
... the Baggot Hamiltonian, as β12 < 0 and λ > 0 the 1:1 resonance width actually decreases as the actions I1 , I2 get larger. Note also that we do not explicitly consider secondary resonances since we are interested only in the large-scale structure of the classical phase space (i.e., intersection of t ...
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... Figure 2. Representation of a coherent state in phase space by its Wigner function. The state has a field amplitude a ¼ jaj exp (if); the integration over one quadrature yields the probabilities to measure specific values for the conjugate quadrature as indicated in the figure. The corresponding probab ...
... Figure 2. Representation of a coherent state in phase space by its Wigner function. The state has a field amplitude a ¼ jaj exp (if); the integration over one quadrature yields the probabilities to measure specific values for the conjugate quadrature as indicated in the figure. The corresponding probab ...
File
... positron, illustrated here. Since energy and momentum must be conserved, the particles are simply transformed into new particles. They do not disappear from existence. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair ...
... positron, illustrated here. Since energy and momentum must be conserved, the particles are simply transformed into new particles. They do not disappear from existence. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair ...
The Schrödinger equation Combining the classical Hamilton
... solutions Xn(x) increases with the energy (compare with a string). The energies (eigenvalues) grow quadratically as a function of n, Ex(n) ∝ n2, and the lowest energy is higher than the potential energy minimum, Ex(n = 1) > 0. The ‘particle in a 1-dimensional box’ has at least this energy, even at t ...
... solutions Xn(x) increases with the energy (compare with a string). The energies (eigenvalues) grow quadratically as a function of n, Ex(n) ∝ n2, and the lowest energy is higher than the potential energy minimum, Ex(n = 1) > 0. The ‘particle in a 1-dimensional box’ has at least this energy, even at t ...
Diapositiva 1 - Indico - Universidad de los Andes
... (iii) APPLICATIONS An intuitive picture (delay due to the creation and propagation of a resonance): ...
... (iii) APPLICATIONS An intuitive picture (delay due to the creation and propagation of a resonance): ...
Lecture I
... Let us describe classical properties of the system before we analyze quantum properties. We’ll consider a Triply Resonant OPO (TR-OPO) in a ring cavity (for simplicity). a0in a1out ...
... Let us describe classical properties of the system before we analyze quantum properties. We’ll consider a Triply Resonant OPO (TR-OPO) in a ring cavity (for simplicity). a0in a1out ...
Ultralow threshold laser using a single quantum dot and a
... emit a photon after an average lifetime t sp . Afterwards, another electron-hole pair is pumped into the QD, and the sequence repeats. The average spontaneous emission rate will thus be N A / t sp , where the inversion parameter N A is the average probability over time that the QD contains an electr ...
... emit a photon after an average lifetime t sp . Afterwards, another electron-hole pair is pumped into the QD, and the sequence repeats. The average spontaneous emission rate will thus be N A / t sp , where the inversion parameter N A is the average probability over time that the QD contains an electr ...
The Wave Function
... The Heisenberg relation has an immediate interpretation. It tells us that we cannot determine, from knowledge of the wave function alone, the exact position and momentum of a particle at the same time. In the extreme case that ∆x = 0, then the position uncertainty is zero, but Eq. (3.14) tells us th ...
... The Heisenberg relation has an immediate interpretation. It tells us that we cannot determine, from knowledge of the wave function alone, the exact position and momentum of a particle at the same time. In the extreme case that ∆x = 0, then the position uncertainty is zero, but Eq. (3.14) tells us th ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.