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Open AccessSymplectic Quantization III: Non-relativistic Limit
First of all we shortly illustrate how the symplectic quantization scheme (Gradenigo and Livi, Found Phys 51(3):66, 2021) can be applied to a relativistic field theory with self-interaction. Taking inspiration...
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Article
Open AccessCondensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation
We study the condensate and superfluid fraction of a homogeneous gas of weakly interacting bosons in three spatial dimensions by adopting a self-consistent Popov approximation, comparing this approach with oth...
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Article
Open AccessAtomic soliton transmission and induced collapse in scattering from a narrow barrier
We report systematic numerical simulations of the collision of a bright matter-wave soliton made of Bose-condensed alkali-metal atoms through a narrow potential barrier by using the three-dimensional Gross–Pit...
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Article
Open AccessFokker-Planck equations for a trapped particle in a quantum-thermal Ohmic bath: general theory and applications to Josephson junctions
We consider a particle trapped by a generic external potential and under the influence of a quantum-thermal Ohmic bath. Starting from the Langevin equation, we derive the corresponding Schwinger-Keldysh action...
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Article
Low-dimensional quantum gases in curved geometries
Atomic gases confined in curved geometries are characterized by distinctive features that are absent in their flat counterparts, such as periodic boundaries, local curvature and nontrivial topologies. The rece...
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Quantum Properties of Light
In this chapter we discuss the three main empirical phenomena which, for the first time, emphasized the quantum nature of light. These phenomena are the black-body radiation, the photoelectric effect, and the ...
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Classical Statistical Mechanics
In this chapter we first discuss the kinetic theory of ideal gases and the Maxwell distribution of velocities at thermal equilibrium. Then we consider the more general Maxwell-Boltzmann distribution of non-int...
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Wavefunction of a Quantum Particle
In this chapter we introduce the time-dependent Schrödinger equation, obtained in 1926 by Erwin Schrödinger from the revolutionary idea of De Broglie to associate to each particle, and in particular to the ele...
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Solvable Problems in Quantum Mechanics
In this chapter we consider relevant applications of quantum mechanics in one spatial dimension. Among them, the quantum particle in a box, in a harmonic potential, and in a double-well potential. We also disc...
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Quantum Mechanics of Many-Body Systems
In this chapter we analyze atoms with many electrons and, more generally, systems with many interacting identical particles. We consider the general properties of many identical particles with their bosonic or...
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Special and General Relativity
In this chapter we review the main results of the theory of special relativity, which was developed by Einstein in 1905. Special relativity has a wide range of consequences which have been confirmed by experim...
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Quantum Properties of Matter
In this chapter we analyze empirical phenomena which are explained by taking into account the quantum nature of matter. We investigate the peculiar behavior shown by the heat capacity in solids at low temperat...
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Axiomatization of Quantum Mechanics
In this chapter we discuss the matrix mechanics of Born, Jordan, and Heisenberg, and then we analyze the basic axioms of quantum mechanics, which were formulated in the seminal books of Dirac and von Neumann. ...
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Modern Quantum Physics of Atoms
In this chapter we analyze the quantum mechanics of the hydrogen atom by using the three-dimensional Schrödinger equation. We also introduce the spin of the electron, giving a rigorous theoretical justificatio...
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Quantum Statistical Mechanics
In this chapter we discuss elements of quantum statistical mechanics. In the first chapter we have seen that statistical mechanics aims to describe macroscopic properties of complex systems starting from their...
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Article
Open AccessShift of the critical temperature in superconductors: a self-consistent approach
Within the Ginzburg-Landau functional framework for the superconducting transition, we analyze the fluctuation-driven shift of the critical temperature. In addition to the order parameter fluctuations, we also...
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