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This work investigates the implications of relaxing the measurement independence assumption in Bell's theorem by introducing a new class of local deterministic models that account for both particle preparation and measurement settings. Our model reproduces the quantum mechanical predictions under the assumption of relaxed measurement independence, demonstrating that the statistical independence of measurement settings does not necessarily preclude underlying correlations. Our findings highlight the nuanced relationship between local determinism and quantum mechanics, offering new insights into the nature of quantum correlations and hidden variables.

We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions. Since the final position of the particle depends on these initial conditions, convolving the Gaussian distributions associated with these initial conditions gives us the distribution of the final positions. In the quantum scenario, using an initial Gaussian wave packet, the temporal evolution provides the final wave function, and from it, the quantum probability density. We find that the quantum probability density coincides with the classical normal distribution of the particle's final position obtained from the convolution theorem. However, for superpositions of Gaussian distributions, the classical and quantum results deviate due to quantum interference. To address this issue, we propose a novel approach to recover the classical distribution from the quantum one. This approach involves removing the quantum interference effects through truncated Fourier analysis. These results are consistent with modern quantum decoherence theory. This comprehensive analysis enhances our understanding of the classical-quantum correspondence and the mechanisms underlying the emergence of classicality from quantum systems.

Interesting phenomena occur when an eccentric rigid body rolls on an inclined or horizontal plane. For example, a variety of motions between rolling and sliding are exhibited until suddenly a jump occurs. We provide a detailed theoretical description of the jump effect for a general eccentric cylinder. Before the jump, when the cylinder moves along the ramp, we can assume a pure rolling motion. However, it turns out that when the cylinder reaches its jumping position, both the normal and static frictional forces approach zero. Thus, it seems that there will no longer be sufficient force to maintain rolling without slip. In order to have a jump without slipping, we prove that the parameters that characterize the dynamic behavior of the cylinder must belong to some restricted region.

We study signatures of physical constraints on free rotations of rigid bodies. We show analytically that the physical or non-physical nature of the moments of inertia of a system can be detected by qualitative changes both in the Montgomery Phase and in the Tennis Racket Effect., Comment: 28 pages, 8 figures

We study in detail the evaluation of the gauge invariant overlap for analytic solutions constructed out of elements in the $KBc$ algebra in open string field theory. We compute this gauge invariant observable using analytical and numerical techniques based on the sliver frame $\mathcal{L}_0$ and traditional Virasoro $L_0$ level expansions of the solutions., Comment: 25 pages

Based on the level truncation scheme, we develop a new numerical method to evaluate the tachyon vacuum solution in the Schnabl gauge up to level $L=24$. We confirm the prediction that the energy associated to this numerical solution has a local minimum at level $L=12$. Extrapolating the energy data of $L \leq 24$ to infinite level, we observe that the energy goes towards the analytical value $-1$, nevertheless the precision of the extrapolation is lower than in the Siegel gauge. Furthermore, we analyze the Ellwood invariant and show that its value converges monotonically towards the expected analytical result. We also study the tachyon vacuum expectation value (vev) and some other coefficients of the solution. Finally, some consistency checks of the solution are performed, and we briefly discuss the search for other Schnabl gauge numerical solutions., Comment: 31 pages, 3 figures, appendix A added

Using traditional Virasoro $L_0$ level-truncation computations, we evaluate the open bosonic string field theory action up to level $(10,30)$. Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value $-1$ at level $L=6$. Extrapolating the level-truncation data for $L\leq 10$ to estimate the vacuum energies for $L > 10$, we predict that the energy reaches a minimum value at $L \sim 12$, and then turns back to approach $-1$ asymptotically as $L \rightarrow \infty$. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at $L \sim 26$, and then turns back to approach the expected analytical result as $L \rightarrow \infty$., Comment: 37 pages, 9 figures, some typos corrected

We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by expanding the solution in the basis of the curly $\mathcal{L}_0$ and the traditional $L_0$ eigenstates, we evaluate numerically the vacuum energy and obtain a result in agreement with Sen's conjecture., Comment: 20 pages; one subsection added

Performing a gauge transformation of a simple identity-like solution of superstring field theory, we construct a one-parameter family of solutions, and by evaluating the energy associated to this family, we show that for most of the values of the parameter the solution represents the tachyon vacuum, except for two isolated singular points where the solution becomes the perturbative vacuum and the half brane solution., Comment: 23 pages; the title and the abstract have been changed; section 6 has been extended; an appendix has been added

We evaluate the vacuum energy of a simple tachyon vacuum solution using the level truncation scheme in cubic superstring field theory. By truncating the standard Virasoro $L_0$ level expansion of the solution, we obtain a value of the vacuum energy in agreement with Sen's first conjecture., Comment: 20 pages, extra factor 2/\pi deleted from equation (3.2), some typos corrected

In a previous paper, we have studied multi-brane solutions in the context of cubic superstring field theory. The kinetic term of the action was computed for these multi-brane solutions, and for the evaluation of the energy, the equation of motion contracted with the solutions itself was simply assumed to be satisfied. In this paper, we compute the cubic term of the action and discuss the validity of the previous assumption. Additionally, we evaluate the Ellwood's gauge invariant observable., Comment: 17 pages; comments added

Using the elements of the so-called $KBc\gamma$ subalgebra, we study a class of analytic solutions depending on a single function $F(K)$ in the modified cubic superstring field theory. We compute the energy associated to these solutions and show that the result can be expressed in terms of a contour integral. For a particular choice of the function $F(K)$, we show that the energy is given by integer multiples of a single D-brane tension., Comment: 14 pages, some typos corrected

We evaluate the vacuum energy of regularized identity based solutions through level truncation computations in open bosonic string field theory. We show that the level truncated solutions bring a value of the vacuum energy expected for the tachyon vacuum in agreement with Sen's first conjecture., Comment: 22 pages, comments added, one table added

Conservation laws have provided an elegant and efficient tool to evaluate the open string field theory interaction vertex, they have been originally implemented in the case where the string field is expanded in the Virasoro basis. In this work we derive conservation laws in the case where the string field is expanded in the so-called sliver $\mathcal{L}_0$-basis. As an application of these conservation laws derived in the sliver frame, we compute the open string field action relevant to the tachyon condensation and in order to present not only an illustration but also an additional information, we evaluate the action without imposing a gauge choice., Comment: 26 pages, some typos fixed, comments added, references added

We analyze the consistency of the recently proposed regularization of an identity based solution in open bosonic string field theory. We show that the equation of motion is satisfied when it is contracted with the regularized solution itself. Additionally, we propose a similar regularization of an identity based solution in the modified cubic superstring field theory., Comment: 24 pages, two subsections added, two references added

We study a new set of identity-based solutions to analyze the problem of tachyon condensation in open bosonic string field theory and cubic superstring field theory. Even though these identity-based solutions seem to be trivial, it turns out that after performing a suitable gauge transformation, we are left with the known Erler-Schnabl-type solutions which correctly reproduce the value of the D-brane tension. This result shows explicitly that how a seemingly trivial solution can generate a non-trivial configuration which precisely represents to the tachyon vacuum., Comment: 22 pages, references added, appendix added, 2 subsections added

We evaluate the tachyon potential in the Schnabl gauge through off-shell computations in the sliver frame. As an application of the results of our computations, we provide a strong evidence that Schnabl's analytic solution for tachyon condensation in open string field theory represents a saddle point configuration of the full tachyon potential. Additionally we verify that Schnabl's analytic solution lies on the minimum of the effective tachyon potential., Comment: v1: 19 pages, 1 figure, 1 table; v2: 20 pages, 1 figure, 2 tables, 1 reference added, comments added; v3: 21 pages, 1 figure, 2 tables, 4 references added, comments added

We evaluate the cubic interaction term in the action of open bosonic string field theory for Schnabl's solution written in terms of Bernoulli numbers. This computation provides us with a new evidence for the fact that the string field equation of motion is satisfied when it is contracted with the solution itself., Comment: 13 pages, added references and fixed typos

In a recent paper, the partition function (character) of ten-dimensional pure spinor worldsheet variables was calculated explicitly up to the fifth mass-level. In this letter, we propose a novel application of Pade approximants as a tool for computing the character of pure spinors. We get results up to the twelfth mass-level. This work is a first step towards an explicit construction of the complete pure spinor partition function., Comment: 16 pages

We clarify the structure of the Hilbert space of curved \beta\gamma systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work., Comment: 45 pages

We explicitly compute up to the fifth mass-level the partition function of ten-dimensional pure spinor worldsheet variables including the spin dependence. After adding the contribution from the (x^{\mu}, \theta^{\alpha}, p_{\alpha}) matter variables, we reproduce the massive superstring spectrum. Even though pure spinor variables are bosonic, the pure spinor partition function contains fermionic states which first appear at the second mass-level. These fermionic states come from functions which are not globally defined in pure spinor space, and are related to the b ghost in the pure spinor formalism. This result clarifies the proper definition of the Hilbert space for pure spinor variables., Comment: 81 pages