搜索结果：Schrdingers

We study the dynamics of multiparticle Carroll-Schrödinger (CS) quantum systems in $1{+}1$ dimensions, where $x$ acts as the evolution variable and $t$ as the configuration coordinate. We derive the $N$-body theory on equal-$x$ slices as the Carrollian limit of a relativistic multi-time Klein-Gordon model, introducing temporal interactions via minimal coupling to the temporal energy operators. An $x$-dependent gauge transformation maps this to an equivalent description with explicit many-body potentials, illustrated by a temporal coupled-oscillator model that exhibits synchronization. Adopting a complementary spatial viewpoint with a static potential $U_{\!tot}(\mathbf x)$, we show that the evolution is driven by the collective force $\sum_j\partial_{x_j}U_{\!tot}$; for any translation-invariant interaction (such as a regularized Coulomb potential), these internal forces cancel, rendering the collective dynamics free and highlighting Carrollian ultralocality. We also construct a coordinate duality mapping separable Schrödinger Hamiltonians to CS generators via Schwarzian derivatives. Exchange symmetry is formulated in the time domain, yielding temporal bunching for bosons and antib

After publishing the derivation from the classical Bloch equation to the quantum von Neumann equation to the Schrdinger-Pauli equation for spin-$\tfrac{1}{2}$, we proposed renaming the Bloch equation to the Majorana-Bloch equation because Majorana's work predated Bloch's in the presentation of the Bloch equation by 14 years. Here, we first generalize our previous derivation to higher spins or angular momenta in coherent pure states. Using the polynomial representation of the coherent-state projector, we derive an invertible mapping from the Majorana-Bloch equation to the von Neumann equation, establishing a one-to-one correspondence between these two formalisms. Application of the Ehrenfest theorem also shows that expectation values in these states reproduce the classical equation of motion as expected. Then, we obtain arbitrary spin-$s$ states by symmetrizing tensor products of spin-$\tfrac{1}{2}$ primitives, in accordance with the Majorana construction or the Schur-Weyl duality.

We consider the dispersion managed nonlinear Schrdinger equations with quintic and cubic nonlinearities in one and two dimensions, respectively. We prove the global well-posedness and scattering in $L_x^2$ for small initial data employing the $U^p$ and $V^p$ spaces.

A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its suited to capture the cylindrical/conical symmetry associated with the cosmic string, providing a more appropriate description of the physical system. After solving Schrdinger's equation, we calculate the eigenenergies, probability distribution function, and expected values for the hydrogen atom with logarithmic potential under the influence of the topological defect. The calculations for the 2D hydrogen atom are performed for the first time using the Finite Difference Method. The results are presented through graphics, tables, and diagrams to elucidate the system's physical properties. We have verified that our calculations agree with a linear variational method result. Our model leads to an interesting analogy with excitons in a two-dimensional monolayer semiconductor located within a specific semiconductor region. To elucidate this analogy, we present and discuss some interaction potentials and their exciton eigenstates by comparing them with th

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New studies suggest consciousness can't be judged solely by behavior, whether it's a chatbot discussing philosophy or a bee searching for nectar。 Researchers are increasingly focusing on the internal mechanisms of brains and computers, concluding that today's AI is likely not conscious while leaving open the possibility for both conscious insects a

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Researchers have discovered how microscopic imperfections and atomic vibrations can be used to control a powerful quantum effect in an advanced material。 The effect can turn alternating electrical signals from the environment directly into the kind of current electronic devices need, without traditional components。 As temperature changes, the signa

Scientists have uncovered unexpected quantum complexity inside cobalt, a metal long thought to be fully understood。 Advanced measurements revealed a dense network of topological electronic states that remain robust at room temperature。 These states enable extremely fast electron behavior and can be switched or controlled using magnetism

For more than a century, pianists and music teachers have argued over whether a performer’s touch can actually change the tone color of a piano note — and now scientists say the answer is yes。 Using a cutting-edge sensor system that tracked piano key movements at 1,000 frames per second, researchers discovered that elite pianists subtly manipulate

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NASA’s futuristic X-59 jet is about to face its biggest challenge yet: breaking the sound barrier for the first time。 After a successful series of test flights that pushed the aircraft to near-supersonic speeds, engineers are preparing to fly it faster than Mach 1 and eventually up to Mach 1。6 at 60,000 feet

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Researchers discovered a way to reverse the direction of energy flow in turbulence, challenging a theory that has stood for more than 80 years。 The finding could open new possibilities for controlling ocean currents, improving medical technologies, and enhancing climate forecasting