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Classical and quantum dynamics on p
... consciousness cannot be explained by the formalism of the classical cognitive mechanics. To explain this phenomenon, we develop a variant of quantum cognitive mechanics. In this model an idea moves in mental space not only due to classical information forces (which can be in principle reduced to the ...
... consciousness cannot be explained by the formalism of the classical cognitive mechanics. To explain this phenomenon, we develop a variant of quantum cognitive mechanics. In this model an idea moves in mental space not only due to classical information forces (which can be in principle reduced to the ...
Why Philosophers Should Care About Computational Complexity Scott Aaronson
... To forestall misunderstandings, let me add a note of humility before going further. This essay will touch on many problems that philosophers have debated for generations, such as strong AI, the problem of induction, the relation between syntax and semantics, and the interpretation of quantum mechani ...
... To forestall misunderstandings, let me add a note of humility before going further. This essay will touch on many problems that philosophers have debated for generations, such as strong AI, the problem of induction, the relation between syntax and semantics, and the interpretation of quantum mechani ...
Phys. Chem. Chem. Phys. 14, 9411-20
... AQS instead of DQS due to the difficulty in performing a DQS. Therefore, the arguments below will mainly apply to AQS, although some of them could also be used on DQS. 2.2.1 Preparing the quantum state into an initial state. In principle, there are two ways to simulate a chemical system.65,66 One is t ...
... AQS instead of DQS due to the difficulty in performing a DQS. Therefore, the arguments below will mainly apply to AQS, although some of them could also be used on DQS. 2.2.1 Preparing the quantum state into an initial state. In principle, there are two ways to simulate a chemical system.65,66 One is t ...
Numerical Renormalization Group Study of Random Transverse
... magnets with an Ising symmetry. The reason for this, as pointed out by Fisher 2) only recently, is a novel fixed point behavior of these systems under renormalization, namely one which is totally determined by the randomness and its geometric properties: the so-called infinite randomness fixed point. ...
... magnets with an Ising symmetry. The reason for this, as pointed out by Fisher 2) only recently, is a novel fixed point behavior of these systems under renormalization, namely one which is totally determined by the randomness and its geometric properties: the so-called infinite randomness fixed point. ...
Simulating Charge Stability Diagrams for Double and Triple
... At the interface between the two different materials a two dimensional electron gas (2DEG) forms. To further confine the other two dimensions of motion we apply voltages to the gates to create potential wells and trap some target number of electrons. We utilize a quantum point contact (QPC) to deter ...
... At the interface between the two different materials a two dimensional electron gas (2DEG) forms. To further confine the other two dimensions of motion we apply voltages to the gates to create potential wells and trap some target number of electrons. We utilize a quantum point contact (QPC) to deter ...
Lecture 1: Elementary quantum algorithms
... qubit if the control qubit is in the state |1〉. Otherwise it does nothing. ...
... qubit if the control qubit is in the state |1〉. Otherwise it does nothing. ...
Feynman-Kac formula for L´evy processes and semiclassical (Euclidean) momentum representation
... (semigroup) method to prove the existence (and even the uniqueness) of a solution for (1.3) and to induce a Feynman-Kac type formula for the solution simultaneously. It is also known that the semigroup method (with infinitesimal generator) only works for (at least) bounded rates. In order to deal wi ...
... (semigroup) method to prove the existence (and even the uniqueness) of a solution for (1.3) and to induce a Feynman-Kac type formula for the solution simultaneously. It is also known that the semigroup method (with infinitesimal generator) only works for (at least) bounded rates. In order to deal wi ...
Normal and Anomalous Diffusion: A Tutorial
... core needs to reach the surface of the Sun. From Eq. (5), we have N = (R/ℓ)2 and since the Sun’s radius is ∼ 1010 cm and the characteristic step (taken into account the density in the solar interior) is ∼ 1 cm, we conclude that photons make 1020 steps before exiting from the Sun’s surface (this can ...
... core needs to reach the surface of the Sun. From Eq. (5), we have N = (R/ℓ)2 and since the Sun’s radius is ∼ 1010 cm and the characteristic step (taken into account the density in the solar interior) is ∼ 1 cm, we conclude that photons make 1020 steps before exiting from the Sun’s surface (this can ...
Coupled-mode theory for general free-space resonant scattering of waves
... the scatterer’s size or radial composition. Hence, only one multipole component of the incident plane wave was scattered at resonance. Now, if we consider an arbitrary resonant scatterer 共not necessarily of spherical or cylindrical symmetry兲, such that its size is much smaller than the wavelength of ...
... the scatterer’s size or radial composition. Hence, only one multipole component of the incident plane wave was scattered at resonance. Now, if we consider an arbitrary resonant scatterer 共not necessarily of spherical or cylindrical symmetry兲, such that its size is much smaller than the wavelength of ...
A Theoretical Study of Atomic Trimers in the Critical Stability Region
... more in Chapter 2. a qualitative discussion on Efimov states see Chapter 3. 6 See more details in Chapter 2. 7 See the definition of a Borromean system in Chapter 3. 8 Halos were first discovered in the nuclear domain, see more in Chapter 3. 9 In fact the above mentioned atomic halo trimers dissocia ...
... more in Chapter 2. a qualitative discussion on Efimov states see Chapter 3. 6 See more details in Chapter 2. 7 See the definition of a Borromean system in Chapter 3. 8 Halos were first discovered in the nuclear domain, see more in Chapter 3. 9 In fact the above mentioned atomic halo trimers dissocia ...
Effect of disorder on quantum phase transitions in
... regions of the phase diagram to the left and right of the dashed line in Fig. 1. ~The commensurate case also occurs on the vertical line h50: then k 0 5 p /2). ...
... regions of the phase diagram to the left and right of the dashed line in Fig. 1. ~The commensurate case also occurs on the vertical line h50: then k 0 5 p /2). ...
Quantum computing: An IBM perspective
... control-and-detection circuitry [41].These resonators have permitted a very precise quantum coupling to be achieved between qubits, so that, for example, highly entangled ...
... control-and-detection circuitry [41].These resonators have permitted a very precise quantum coupling to be achieved between qubits, so that, for example, highly entangled ...
Molecular structure calculations: A unified quantum
... Instead of re-expressing this Hamiltonian using translational, orientational, and internal coordinates, we use Cartesian coordinates and set up a trial wave function in a variational procedure as a linear combination of symmetryadapted basis functions, which are angular momentum (total spatial angul ...
... Instead of re-expressing this Hamiltonian using translational, orientational, and internal coordinates, we use Cartesian coordinates and set up a trial wave function in a variational procedure as a linear combination of symmetryadapted basis functions, which are angular momentum (total spatial angul ...
Investigating incompatibility: How to reconcile complementarity with EPR C
... This is not just a restriction of our knowledge. It is not asserted that we occasionally cannot know the position with a precision <1cm. and then conclude, by some kind of positivistic reasoning, that more precise statements are ‘meaningless’. Quite the contrary, it is asserted that [...] once these ...
... This is not just a restriction of our knowledge. It is not asserted that we occasionally cannot know the position with a precision <1cm. and then conclude, by some kind of positivistic reasoning, that more precise statements are ‘meaningless’. Quite the contrary, it is asserted that [...] once these ...
lecture notes on applied mathematics
... choice of the system. The independence of a model from the system of units used to measure the quantities that appear in it therefore corresponds to a scale-invariance of the model. Remark 2.1. Sometimes it is convenient to use a logarithmic scale of units instead of a linear scale (such as the Rich ...
... choice of the system. The independence of a model from the system of units used to measure the quantities that appear in it therefore corresponds to a scale-invariance of the model. Remark 2.1. Sometimes it is convenient to use a logarithmic scale of units instead of a linear scale (such as the Rich ...
Probability amplitude
![](https://commons.wikimedia.org/wiki/Special:FilePath/Hydrogen_eigenstate_n5_l2_m1.png?width=300)
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.